// BEGIN: ../sakumon/bonsai/reusable_lazy_segment_tree/main.cpp
#line 1 "..::sakumon::bonsai::reusable_lazy_segment_tree::main.cpp"
// BEGIN: pch.hpp
#line 3 "pch.hpp"

#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif

#define dump(...)
#define CPP_DUMP_SET_OPTION(...)
#define CPP_DUMP_DEFINE_EXPORT_OBJECT(...)
#define CPP_DUMP_DEFINE_EXPORT_ENUM(...)
#define CPP_DUMP_DEFINE_DANGEROUS_EXPORT_OBJECT(...)

// BEGIN: template.hpp
#line 3 "template.hpp"

#include <algorithm>
#include <any>
#include <array>
#include <atomic>
#include <barrier>
#include <bit>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cerrno>
#include <cfenv>
#include <cfloat>
#include <charconv>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <clocale>
#include <cmath>
#include <codecvt>
#include <compare>
#include <complex>
#include <concepts>
#include <condition_variable>
#include <coroutine>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstring>
#include <ctime>
#include <cuchar>
#include <cwchar>
#include <cwctype>
#include <deque>
#include <exception>
#include <execution>
#include <filesystem>
#include <format>
#include <forward_list>
#include <fstream>
#include <functional>
#include <future>
#include <iomanip>
#include <initializer_list>
#include <iostream>
#include <ios>
#include <iosfwd>
#include <istream>
#include <iterator>
#include <latch>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <memory_resource>
#include <mutex>
#include <new>
#include <numbers>
#include <numeric>
#include <optional>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <semaphore>
#include <set>
#include <shared_mutex>
#include <source_location>
#include <span>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <stop_token>
#include <streambuf>
#include <string>
#include <string_view>
#include <syncstream>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <valarray>
#include <variant>
#include <vector>
#include <version>

// BEGIN: utilities/fast_io.hpp
#line 3 "utilities::fast_io.hpp"

#include <algorithm>
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#include <utility>
#include <unistd.h>

namespace m1une {
namespace utilities {
namespace internal {

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {}

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_position > buffer_size - 64) flush();
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) _buffer[_position++] = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(_buffer + _position, digits, 4);
            _position += 4;
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une

// END: utilities/fast_io.hpp
#line 103 "template.hpp"
using namespace std;

namespace m1une {
namespace template_io {

inline utilities::FastInput& input() {
    static utilities::FastInput instance;
    return instance;
}

inline utilities::FastOutput& output() {
    static utilities::FastOutput instance;
    return instance;
}

}  // namespace template_io
}  // namespace m1une

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
#ifdef __SIZEOF_FLOAT128__
using f128 = __float128;
#endif

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<int, int>;
using pl = pair<ll, ll>;
using vi = vector<int>;
using vl = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
using vvi = vvc<int>;
using vvl = vvc<ll>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pqg = std::priority_queue<T, vector<T>, greater<T>>;
template <class T, class U>
using umap = unordered_map<T, U>;

// template <typename K>
// using tree = __gnu_pbds::tree<K, __gnu_pbds::null_type, std::less<>,
//                               __gnu_pbds::rb_tree_tag,
//                               __gnu_pbds::tree_order_statistics_node_update>;

#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
    vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)         \
    vector<vector<vector<vector<type>>>> name( \
        a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d

// FOR(a) :=  for (ll _ = 0; _ < (ll)a; ++_)
// FOR(i, a) := for (ll i = 0; i < (ll)a; ++i)
// FOR(i, a, b) := for (ll i = a; i < (ll)b; ++i)
// FOR(i, a, b, c) := for (ll i = a; i < (ll)b; i += (c))
// FOR_R(a) := for (ll i = (a) - 1; i >= 0; --i)
// FOR_R(i, a) := for (ll i = (a) - 1; i >= 0; --i)
// FOR_R(i, a, b) := for (ll i = (b) - 1; i >= (ll)a; --i)
#define FOR1(a) for (ll _ = 0; _ < (ll)a; ++_)
#define FOR2(i, a) for (ll i = 0; i < (ll)a; ++i)
#define FOR3(i, a, b) for (ll i = a; i < (ll)b; ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < (ll)b; i += (c))
#define FOR1_R(a) for (ll i = (a) - 1; i >= 0; --i)
#define FOR2_R(i, a) for (ll i = (a) - 1; i >= 0; --i)
#define FOR3_R(i, a, b) for (ll i = (b) - 1; i >= (ll)a; --i)
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FORI1(a) for (int _ = 0; _ < (int)a; ++_)
#define FORI2(i, a) for (int i = 0; i < (int)a; ++i)
#define FORI3(i, a, b) for (int i = a; i < (int)b; ++i)
#define FORI4(i, a, b, c) for (int i = a; i < (int)b; i += (c))
#define FORI1_R(a) for (int i = (a) - 1; i >= 0; --i)
#define FORI2_R(i, a) for (int i = (a) - 1; i >= 0; --i)
#define FORI3_R(i, a, b) for (int i = (b) - 1; i >= (int)a; --i)
#define FORI(...) overload4(__VA_ARGS__, FORI4, FORI3, FORI2, FORI1)(__VA_ARGS__)
#define FORI_R(...) overload3(__VA_ARGS__, FORI3_R, FORI2_R, FORI1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (int t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()

int popcnt(int x) {
    return __builtin_popcount(x);
}
int popcnt(u32 x) {
    return __builtin_popcount(x);
}
int popcnt(ll x) {
    return __builtin_popcountll(x);
}
int popcnt(u64 x) {
    return __builtin_popcountll(x);
}
int popcnt_mod_2(int x) {
    return __builtin_parity(x);
}
int popcnt_mod_2(u32 x) {
    return __builtin_parity(x);
}
int popcnt_mod_2(ll x) {
    return __builtin_parityll(x);
}
int popcnt_mod_2(u64 x) {
    return __builtin_parityll(x);
}
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) {
    return (x == 0 ? -1 : 31 - __builtin_clz(x));
}
int topbit(u32 x) {
    return (x == 0 ? -1 : 31 - __builtin_clz(x));
}
int topbit(ll x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
int topbit(u64 x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) {
    return (x == 0 ? -1 : __builtin_ctz(x));
}
int lowbit(u32 x) {
    return (x == 0 ? -1 : __builtin_ctz(x));
}
int lowbit(ll x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}
int lowbit(u64 x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

template <typename T>
T floor(T a, T b) {
    return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
    return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
    return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
    T q = floor(x, y);
    return {q, x - q * y};
}

template <typename T, typename U>
T POW(U x_, int n) {
    T x = x_;
    T ret = 1;
    while (n > 0) {
        if (n & 1) ret *= x;
        x *= x;
        n >>= 1;
    }
    return ret;
}

template <typename T, typename U>
T SUM(const vector<U>& A) {
    T sm = 0;
    for (auto&& a : A) sm += a;
    return sm;
}

#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <class T, class S>
inline bool chmax(T& a, const S& b) {
    return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T& a, const S& b) {
    return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string& S, char first_char) {
    vc<int> A(S.size());
    FOR(i, S.size()) {
        A[i] = (S[i] != '?' ? S[i] - first_char : -1);
    }
    return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U>& A, int off = 1) {
    int N = A.size();
    vector<T> B(N + 1);
    FOR(i, N) {
        B[i + 1] = B[i] + A[i];
    }
    if (off == 0) B.erase(B.begin());
    return B;
}

template <typename T>
vector<int> argsort(const vector<T>& A) {
    vector<int> ids(A.size());
    iota(all(ids), 0);
    sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
    return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T>& A, const vc<int>& I) {
    vc<T> B(I.size());
    FOR(i, I.size()) B[i] = A[I[i]];
    return B;
}

template <class... T>
constexpr auto min(T... a) {
    return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T>
constexpr auto max(T... a) {
    return max(initializer_list<common_type_t<T...>>{a...});
}

template <class... Ts>
bool scan(Ts&... values) {
    return m1une::template_io::input().read(values...);
}

template <class... Ts>
void print(const Ts&... values) {
    m1une::template_io::output().println(values...);
}
void YESNO(bool b) {
    m1une::template_io::output().println(b ? "YES" : "NO");
}
void YesNo(bool b) {
    m1une::template_io::output().println(b ? "Yes" : "No");
}
void YES() {
    m1une::template_io::output().println("YES");
}
void NO() {
    m1une::template_io::output().println("NO");
}
void Yes() {
    m1une::template_io::output().println("Yes");
}
void No() {
    m1une::template_io::output().println("No");
}
// END: template.hpp
#line 29 "pch.hpp"

// END: pch.hpp
#line 2 "..::sakumon::bonsai::reusable_lazy_segment_tree::main.cpp"

auto& fastin = m1une::template_io::input();
auto& fastout = m1une::template_io::output();

// BEGIN: beats_acted_monoid/range_bitwise_and_or_range_sum.hpp
#line 3 "beats_acted_monoid::range_bitwise_and_or_range_sum.hpp"

#include <cassert>
#include <limits>
#include <type_traits>

namespace m1une {
namespace beats_acted_monoid {

template <typename T>
struct RangeBitwiseAndOrRangeSumNode {
    T sum;
    T bitwise_and;
    T bitwise_or;
    long long length;
};

// Beats acted monoid for range bitwise AND/OR updates and range sum queries.
template <typename T, int BITS = 30>
struct RangeBitwiseAndOrRangeSum {
    static_assert(
        std::is_integral_v<T> &&
        !std::is_same_v<std::remove_cv_t<T>, bool>
    );
    static_assert(0 < BITS && BITS <= std::numeric_limits<T>::digits);

    using value_type = RangeBitwiseAndOrRangeSumNode<T>;

    // Represents f(x) = (x & and_mask) | or_mask.
    struct operator_type {
        T and_mask;
        T or_mask;
    };

    static constexpr bool commutative = true;
    static constexpr bool operator_commutative = false;

    static constexpr T bit_mask() {
        if constexpr (
            std::is_unsigned_v<T> &&
            BITS == std::numeric_limits<T>::digits
        ) {
            return ~T(0);
        } else {
            return
                (T(1) << (BITS - 1)) |
                ((T(1) << (BITS - 1)) - 1);
        }
    }

    static constexpr value_type id() {
        return {T(0), bit_mask(), T(0), 0};
    }

    static constexpr value_type op(
        const value_type& left,
        const value_type& right
    ) {
        return {
            left.sum + right.sum,
            left.bitwise_and & right.bitwise_and,
            left.bitwise_or | right.bitwise_or,
            left.length + right.length
        };
    }

    static constexpr operator_type op_id() {
        return {bit_mask(), T(0)};
    }

    // Returns f(g(x)).
    static constexpr operator_type op_comp(
        const operator_type& f,
        const operator_type& g
    ) {
        return {
            (f.and_mask & g.and_mask) & bit_mask(),
            ((g.or_mask & f.and_mask) | f.or_mask) & bit_mask()
        };
    }

    static constexpr bool can_apply(
        const operator_type& f,
        const value_type& value
    ) {
        if (value.length == 0) return true;
        T changed = ((~f.and_mask) | f.or_mask) & bit_mask();
        T mixed = value.bitwise_and ^ value.bitwise_or;
        return (changed & mixed) == T(0);
    }

    static constexpr value_type mapping(
        const operator_type& f,
        const value_type& value
    ) {
        assert(can_apply(f, value));
        if (value.length == 0) return value;
        T changed = ((~f.and_mask) | f.or_mask) & bit_mask();
        T old_uniform = value.bitwise_and & changed;
        T new_uniform =
            ((old_uniform & f.and_mask) | f.or_mask) & changed;

        value_type result = value;
        result.sum +=
            (new_uniform - old_uniform) * T(value.length);
        result.bitwise_and =
            ((value.bitwise_and & f.and_mask) | f.or_mask) & bit_mask();
        result.bitwise_or =
            ((value.bitwise_or & f.and_mask) | f.or_mask) & bit_mask();
        return result;
    }

    static constexpr value_type make(const T& value) {
        assert((value & ~bit_mask()) == T(0));
        return {value, value, value, 1};
    }

    static constexpr operator_type make_and(const T& mask) {
        return {mask & bit_mask(), T(0)};
    }

    static constexpr operator_type make_or(const T& mask) {
        return {bit_mask(), mask & bit_mask()};
    }
};

}  // namespace beats_acted_monoid
}  // namespace m1une

// END: beats_acted_monoid/range_bitwise_and_or_range_sum.hpp
#line 7 "..::sakumon::bonsai::reusable_lazy_segment_tree::main.cpp"
// BEGIN: ds/segtree/persistent_segtree_beats.hpp
#line 3 "ds::segtree::persistent_segtree_beats.hpp"

#include <cassert>
#include <concepts>
#include <cstddef>
#include <memory>
#include <utility>
#include <vector>

// BEGIN: ../../beats_acted_monoid/concept.hpp
#line 3 "..::..::beats_acted_monoid::concept.hpp"

#include <concepts>

// BEGIN: ../acted_monoid/concept.hpp
#line 3 "..::acted_monoid::concept.hpp"

#include <concepts>

namespace m1une {
namespace acted_monoid {

// Concept defining the requirements for an Acted Monoid.
template <typename AM>
concept IsActedMonoid = requires(typename AM::value_type a, typename AM::value_type b, typename AM::operator_type f,
                                 typename AM::operator_type g) {
    // 1. Value Monoid
    typename AM::value_type;
    { AM::id() } -> std::same_as<typename AM::value_type>;
    { AM::op(a, b) } -> std::same_as<typename AM::value_type>;

    // 2. Operator Monoid
    typename AM::operator_type;
    { AM::op_id() } -> std::same_as<typename AM::operator_type>;
    { AM::op_comp(f, g) } -> std::same_as<typename AM::operator_type>;  // Composition order: f(g(x))

    // 3. Mapping: Operator x Value -> Value
    { AM::mapping(f, a) } -> std::same_as<typename AM::value_type>;
};

// Concept for acted monoids whose value monoid is a commutative group.
// The value operation must obey commutativity and inverse laws.
template <typename AM>
concept IsCommutativeActedGroup = IsActedMonoid<AM> && requires(typename AM::value_type a) {
    { AM::inv(a) } -> std::same_as<typename AM::value_type>;
};

}  // namespace acted_monoid
}  // namespace m1une

// END: ../acted_monoid/concept.hpp
#line 7 "..::..::beats_acted_monoid::concept.hpp"

namespace m1une {
namespace beats_acted_monoid {

// An acted monoid whose action may require descent before it can be applied.
template <typename AM>
concept IsBeatsActedMonoid = m1une::acted_monoid::IsActedMonoid<AM> &&
    requires(typename AM::value_type x, typename AM::operator_type f) {
        { AM::can_apply(f, x) } -> std::same_as<bool>;
    };

}  // namespace beats_acted_monoid
}  // namespace m1une

// END: ../../beats_acted_monoid/concept.hpp
#line 12 "ds::segtree::persistent_segtree_beats.hpp"
// BEGIN: persistent_node_pool.hpp
#line 3 "persistent_node_pool.hpp"

#include <cassert>
#include <cstddef>
#include <limits>
#include <utility>
#include <vector>

namespace m1une {
namespace ds {
namespace detail {

// Node must have integer `left`, `right`, and `references` members.
template <class Node>
struct PersistentNodePool {
    std::vector<Node> nodes;
    int first_free = 0;
    std::size_t live_nodes = 0;

   private:
    void release_zero(int node) {
        int left = nodes[node].left;
        int right = nodes[node].right;
        nodes[node] = Node();
        nodes[node].left = first_free;
        first_free = node;
        --live_nodes;
        if (left && --nodes[left].references == 0) release_zero(left);
        if (right && --nodes[right].references == 0) release_zero(right);
    }

   public:
    PersistentNodePool() { nodes.emplace_back(); }

    void reserve(std::size_t capacity) { nodes.reserve(capacity + 1); }

    Node& operator[](int node) { return nodes[node]; }

    const Node& operator[](int node) const { return nodes[node]; }

    void retain(int node) {
        if (node) ++nodes[node].references;
    }

    void release(int node) {
        if (!node) return;
        assert(nodes[node].references > 0);
        if (--nodes[node].references == 0) release_zero(node);
    }

    template <class... Args>
    int emplace(Args&&... args) {
        int result;
        if (!first_free) {
            assert(nodes.size() < std::size_t(std::numeric_limits<int>::max()));
            nodes.emplace_back(std::forward<Args>(args)...);
            result = int(nodes.size()) - 1;
        } else {
            result = first_free;
            first_free = nodes[result].left;
            nodes[result] = Node(std::forward<Args>(args)...);
        }
        Node& node = nodes[result];
        node.references = 0;
        retain(node.left);
        retain(node.right);
        ++live_nodes;
        return result;
    }

    int clone(int node) {
        assert(node);
        Node copy = nodes[node];
        return emplace(std::move(copy));
    }

    void replace(int& edge, int node) {
        if (edge == node) return;
        retain(node);
        int old = edge;
        edge = node;
        release(old);
    }

    std::size_t size() const { return live_nodes; }
};

}  // namespace detail
}  // namespace ds
}  // namespace m1une

// END: persistent_node_pool.hpp
#line 13 "ds::segtree::persistent_segtree_beats.hpp"

namespace m1une {
namespace ds {

// A persistent Segment Tree Beats for fallible monoid actions.
template <m1une::beats_acted_monoid::IsBeatsActedMonoid ActedMonoid>
struct PersistentSegtreeBeats {
    using value_type = typename ActedMonoid::value_type;
    using operator_type = typename ActedMonoid::operator_type;
    using T = value_type;
    using F = operator_type;

   private:
    struct Node {
        T val;
        F lazy;
        int left;
        int right;
        int references;
        bool has_lazy;

        Node()
            : val(ActedMonoid::id()),
              lazy(ActedMonoid::op_id()),
              left(0),
              right(0),
              references(0),
              has_lazy(false) {}

        explicit Node(T value)
            : val(std::move(value)),
              lazy(ActedMonoid::op_id()),
              left(0),
              right(0),
              references(0),
              has_lazy(false) {}

        Node(T value, int left_child, int right_child)
            : val(std::move(value)),
              lazy(ActedMonoid::op_id()),
              left(left_child),
              right(right_child),
              references(0),
              has_lazy(false) {}
    };

    using Pool = detail::PersistentNodePool<Node>;

    int _n;
    int _root;
    std::shared_ptr<Pool> _pool;

    explicit PersistentSegtreeBeats(
        int n,
        int root,
        std::shared_ptr<Pool> pool
    ) : _n(n), _root(root), _pool(std::move(pool)) {
        _pool->retain(_root);
    }

    int new_node(const Node& node) const {
        return _pool->emplace(node);
    }

    int new_node(Node&& node) const {
        return _pool->emplace(std::move(node));
    }

    int clone_node(int node) const {
        return _pool->clone(node);
    }

    template <typename U>
    static T make_value(const U& value, int index) {
        if constexpr (requires(U x) { ActedMonoid::make(x); }) {
            return ActedMonoid::make(value);
        } else if constexpr (requires(U x, int i) {
            ActedMonoid::make(x, i);
        }) {
            return ActedMonoid::make(value, index);
        } else {
            return static_cast<T>(value);
        }
    }

    static T mapping_at(const F& f, const T& value, long long ordinal) {
        if constexpr (requires(F g, T x, long long i) {
            ActedMonoid::mapping(g, x, i);
        }) {
            return ActedMonoid::mapping(f, value, ordinal);
        } else {
            return ActedMonoid::mapping(f, value);
        }
    }

    static bool can_apply_at(
        const F& f,
        const T& value,
        long long ordinal
    ) {
        if constexpr (requires(F g, T x, long long i) {
            ActedMonoid::can_apply(g, x, i);
        }) {
            return ActedMonoid::can_apply(f, value, ordinal);
        } else {
            return ActedMonoid::can_apply(f, value);
        }
    }

    static F shift_operator(const F& f, long long ordinal) {
        if constexpr (requires(F g, long long i) {
            ActedMonoid::op_shift(g, i);
        }) {
            return ActedMonoid::op_shift(f, ordinal);
        } else {
            return f;
        }
    }

    int build(int left, int right, const std::vector<T>& values) const {
        if (left == right) return 0;
        if (right - left == 1) return new_node(Node(values[left]));
        int middle = left + (right - left) / 2;
        int left_child = build(left, middle, values);
        int right_child = build(middle, right, values);
        return new_node(Node(
            ActedMonoid::op(
                (*_pool)[left_child].val,
                (*_pool)[right_child].val
            ),
            left_child,
            right_child
        ));
    }

    int build(int left, int right, std::vector<T>& values) const {
        if (left == right) return 0;
        if (right - left == 1) {
            return new_node(Node(std::move(values[left])));
        }
        int middle = left + (right - left) / 2;
        int left_child = build(left, middle, values);
        int right_child = build(middle, right, values);
        return new_node(Node(
            ActedMonoid::op(
                (*_pool)[left_child].val,
                (*_pool)[right_child].val
            ),
            left_child,
            right_child
        ));
    }

    template <typename U>
    int build_from_values(
        int left,
        int right,
        const std::vector<U>& values
    ) const {
        if (left == right) return 0;
        if (right - left == 1) {
            return new_node(Node(make_value(values[left], left)));
        }
        int middle = left + (right - left) / 2;
        int left_child = build_from_values(left, middle, values);
        int right_child = build_from_values(middle, right, values);
        return new_node(Node(
            ActedMonoid::op(
                (*_pool)[left_child].val,
                (*_pool)[right_child].val
            ),
            left_child,
            right_child
        ));
    }

    void update(int node) const {
        Node& current = (*_pool)[node];
        current.val = ActedMonoid::op(
            (*_pool)[current.left].val,
            (*_pool)[current.right].val
        );
    }

    int all_apply_clone(
        int node,
        int left,
        int right,
        const F& f
    ) const {
        int result = clone_node(node);
        Node& current = (*_pool)[result];
        if (can_apply_at(f, current.val, 0)) {
            current.val = mapping_at(f, current.val, 0);
            if (right - left > 1) {
                current.lazy = ActedMonoid::op_comp(f, current.lazy);
                current.has_lazy = true;
            }
            return result;
        }

        assert(right - left > 1);
        push(result, left, right);
        int middle = left + (right - left) / 2;
        int left_child = all_apply_clone(
            (*_pool)[result].left,
            left,
            middle,
            f
        );
        int right_child = all_apply_clone(
            (*_pool)[result].right,
            middle,
            right,
            shift_operator(f, middle - left)
        );
        _pool->replace((*_pool)[result].left, left_child);
        _pool->replace((*_pool)[result].right, right_child);
        update(result);
        return result;
    }

    void push(int node, int left, int right) const {
        if (!(*_pool)[node].has_lazy) return;
        assert(right - left > 1);

        F lazy = (*_pool)[node].lazy;
        int middle = left + (right - left) / 2;
        int left_child = all_apply_clone(
            (*_pool)[node].left,
            left,
            middle,
            lazy
        );
        int right_child = all_apply_clone(
            (*_pool)[node].right,
            middle,
            right,
            shift_operator(lazy, middle - left)
        );
        _pool->replace((*_pool)[node].left, left_child);
        _pool->replace((*_pool)[node].right, right_child);
        Node& current = (*_pool)[node];
        current.lazy = ActedMonoid::op_id();
        current.has_lazy = false;
    }

    int set_node(
        int node,
        int left,
        int right,
        int index,
        T value
    ) const {
        int result = clone_node(node);
        if (right - left == 1) {
            Node& current = (*_pool)[result];
            current.val = std::move(value);
            current.lazy = ActedMonoid::op_id();
            current.has_lazy = false;
            return result;
        }

        push(result, left, right);
        int middle = left + (right - left) / 2;
        if (index < middle) {
            int child = set_node(
                (*_pool)[result].left,
                left,
                middle,
                index,
                std::move(value)
            );
            _pool->replace((*_pool)[result].left, child);
        } else {
            int child = set_node(
                (*_pool)[result].right,
                middle,
                right,
                index,
                std::move(value)
            );
            _pool->replace((*_pool)[result].right, child);
        }
        update(result);
        return result;
    }

    int apply_node(
        int node,
        int left,
        int right,
        int query_left,
        int query_right,
        const F& f
    ) const {
        if (query_right <= left || right <= query_left) return node;
        if (query_left <= left && right <= query_right) {
            return all_apply_clone(
                node,
                left,
                right,
                shift_operator(f, left - query_left)
            );
        }

        int result = clone_node(node);
        push(result, left, right);
        int middle = left + (right - left) / 2;
        int left_child = apply_node(
            (*_pool)[result].left,
            left,
            middle,
            query_left,
            query_right,
            f
        );
        int right_child = apply_node(
            (*_pool)[result].right,
            middle,
            right,
            query_left,
            query_right,
            f
        );
        _pool->replace((*_pool)[result].left, left_child);
        _pool->replace((*_pool)[result].right, right_child);
        update(result);
        return result;
    }

    int copy_range_node(
        int target,
        int source,
        int left,
        int right,
        int query_left,
        int query_right
    ) const {
        if (query_right <= left || right <= query_left) return target;
        if (query_left <= left && right <= query_right) return source;

        int result = clone_node(target);
        int materialized_source = clone_node(source);
        _pool->retain(materialized_source);
        push(result, left, right);
        push(materialized_source, left, right);

        int middle = left + (right - left) / 2;
        int left_child = copy_range_node(
            (*_pool)[result].left,
            (*_pool)[materialized_source].left,
            left,
            middle,
            query_left,
            query_right
        );
        int right_child = copy_range_node(
            (*_pool)[result].right,
            (*_pool)[materialized_source].right,
            middle,
            right,
            query_left,
            query_right
        );
        _pool->replace((*_pool)[result].left, left_child);
        _pool->replace((*_pool)[result].right, right_child);
        update(result);
        _pool->release(materialized_source);
        return result;
    }

    F compose_for_child(
        const F& inherited,
        const Node& node,
        long long ordinal
    ) const {
        F shifted = shift_operator(inherited, ordinal);
        if (!node.has_lazy) return shifted;
        return ActedMonoid::op_comp(
            shifted,
            shift_operator(node.lazy, ordinal)
        );
    }

    T evaluate_node(
        int node,
        int left,
        int right,
        const F& inherited
    ) const {
        const Node& current = (*_pool)[node];
        if (can_apply_at(inherited, current.val, 0)) {
            return mapping_at(inherited, current.val, 0);
        }

        assert(right - left > 1);
        int middle = left + (right - left) / 2;
        return ActedMonoid::op(
            evaluate_node(
                current.left,
                left,
                middle,
                compose_for_child(inherited, current, 0)
            ),
            evaluate_node(
                current.right,
                middle,
                right,
                compose_for_child(inherited, current, middle - left)
            )
        );
    }

    T prod_node(
        int node,
        int left,
        int right,
        int query_left,
        int query_right,
        const F& inherited
    ) const {
        if (query_right <= left || right <= query_left) {
            return ActedMonoid::id();
        }
        if (query_left <= left && right <= query_right) {
            return evaluate_node(node, left, right, inherited);
        }

        const Node& current = (*_pool)[node];
        int middle = left + (right - left) / 2;
        return ActedMonoid::op(
            prod_node(
                current.left,
                left,
                middle,
                query_left,
                query_right,
                compose_for_child(inherited, current, 0)
            ),
            prod_node(
                current.right,
                middle,
                right,
                query_left,
                query_right,
                compose_for_child(inherited, current, middle - left)
            )
        );
    }

    void collect_node(
        int node,
        int left,
        int right,
        int query_left,
        int query_right,
        const F& inherited,
        std::vector<T>& result
    ) const {
        if (query_right <= left || right <= query_left) return;
        const Node& current = (*_pool)[node];
        if (right - left == 1) {
            result.push_back(mapping_at(inherited, current.val, 0));
            return;
        }

        int middle = left + (right - left) / 2;
        collect_node(
            current.left,
            left,
            middle,
            query_left,
            query_right,
            compose_for_child(inherited, current, 0),
            result
        );
        collect_node(
            current.right,
            middle,
            right,
            query_left,
            query_right,
            compose_for_child(inherited, current, middle - left),
            result
        );
    }

    template <class Predicate>
    int max_right_node(
        int node,
        int left,
        int right,
        int query_left,
        T& product,
        const F& inherited,
        Predicate& predicate
    ) const {
        if (right <= query_left) return right;
        if (query_left <= left) {
            T next = ActedMonoid::op(
                product,
                evaluate_node(node, left, right, inherited)
            );
            if (predicate(next)) {
                product = std::move(next);
                return right;
            }
            if (right - left == 1) return left;
        }

        const Node& current = (*_pool)[node];
        int middle = left + (right - left) / 2;
        int result = max_right_node(
            current.left,
            left,
            middle,
            query_left,
            product,
            compose_for_child(inherited, current, 0),
            predicate
        );
        if (result < middle) return result;
        return max_right_node(
            current.right,
            middle,
            right,
            query_left,
            product,
            compose_for_child(inherited, current, middle - left),
            predicate
        );
    }

    template <class Predicate>
    int min_left_node(
        int node,
        int left,
        int right,
        int query_right,
        T& product,
        const F& inherited,
        Predicate& predicate
    ) const {
        if (query_right <= left) return left;
        if (right <= query_right) {
            T next = ActedMonoid::op(
                evaluate_node(node, left, right, inherited),
                product
            );
            if (predicate(next)) {
                product = std::move(next);
                return left;
            }
            if (right - left == 1) return right;
        }

        const Node& current = (*_pool)[node];
        int middle = left + (right - left) / 2;
        int result = min_left_node(
            current.right,
            middle,
            right,
            query_right,
            product,
            compose_for_child(inherited, current, middle - left),
            predicate
        );
        if (middle < result) return result;
        return min_left_node(
            current.left,
            left,
            middle,
            query_right,
            product,
            compose_for_child(inherited, current, 0),
            predicate
        );
    }

   public:
    PersistentSegtreeBeats() : PersistentSegtreeBeats(0) {}

    explicit PersistentSegtreeBeats(int n)
        : _n(n), _root(0), _pool(std::make_shared<Pool>()) {
        assert(0 <= n);
        if (_n > 0) {
            std::vector<T> values(_n, ActedMonoid::id());
            _root = build(0, _n, values);
        }
        _pool->retain(_root);
    }

    explicit PersistentSegtreeBeats(const std::vector<T>& values)
        : _n(int(values.size())),
          _root(0),
          _pool(std::make_shared<Pool>()) {
        _pool->reserve(values.size() * 2);
        if (_n > 0) _root = build(0, _n, values);
        _pool->retain(_root);
    }

    explicit PersistentSegtreeBeats(std::vector<T>&& values)
        : _n(int(values.size())),
          _root(0),
          _pool(std::make_shared<Pool>()) {
        _pool->reserve(values.size() * 2);
        if (_n > 0) _root = build(0, _n, values);
        _pool->retain(_root);
    }

    template <typename U>
    requires (!std::same_as<U, T>) && (
        requires(U x) { ActedMonoid::make(x); } ||
        requires(U x, int i) { ActedMonoid::make(x, i); } ||
        std::convertible_to<U, T>
    )
    explicit PersistentSegtreeBeats(const std::vector<U>& values)
        : _n(int(values.size())),
          _root(0),
          _pool(std::make_shared<Pool>()) {
        _pool->reserve(values.size() * 2);
        if (_n > 0) _root = build_from_values(0, _n, values);
        _pool->retain(_root);
    }

    PersistentSegtreeBeats(const PersistentSegtreeBeats& other)
        : _n(other._n), _root(other._root), _pool(other._pool) {
        if (_pool) _pool->retain(_root);
    }

    PersistentSegtreeBeats(PersistentSegtreeBeats&& other) noexcept
        : _n(other._n),
          _root(other._root),
          _pool(std::move(other._pool)) {
        other._n = 0;
        other._root = 0;
    }

    PersistentSegtreeBeats& operator=(
        const PersistentSegtreeBeats& other
    ) {
        if (this == &other) return *this;
        if (other._pool) other._pool->retain(other._root);
        if (_pool) _pool->release(_root);
        _n = other._n;
        _root = other._root;
        _pool = other._pool;
        return *this;
    }

    PersistentSegtreeBeats& operator=(
        PersistentSegtreeBeats&& other
    ) noexcept {
        if (this == &other) return *this;
        if (_pool) _pool->release(_root);
        _n = other._n;
        _root = other._root;
        _pool = std::move(other._pool);
        other._n = 0;
        other._root = 0;
        return *this;
    }

    ~PersistentSegtreeBeats() {
        if (_pool) _pool->release(_root);
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    void release() {
        if (_pool) _pool->release(_root);
        _pool = std::make_shared<Pool>();
        _root = 0;
        _n = 0;
    }

    std::size_t node_count() const {
        return _pool ? _pool->size() : 0;
    }

    PersistentSegtreeBeats set(int index, T value) const {
        assert(0 <= index && index < _n);
        return PersistentSegtreeBeats(
            _n,
            set_node(_root, 0, _n, index, std::move(value)),
            _pool
        );
    }

    T get(int index) const {
        assert(0 <= index && index < _n);
        return prod(index, index + 1);
    }

    T operator[](int index) const {
        return get(index);
    }

    T prod(int left, int right) const {
        assert(0 <= left && left <= right && right <= _n);
        if (left == right) return ActedMonoid::id();
        return prod_node(
            _root,
            0,
            _n,
            left,
            right,
            ActedMonoid::op_id()
        );
    }

    T all_prod() const {
        return _root ? (*_pool)[_root].val : ActedMonoid::id();
    }

    PersistentSegtreeBeats apply(int index, const F& f) const {
        assert(0 <= index && index < _n);
        return apply(index, index + 1, f);
    }

    PersistentSegtreeBeats apply(
        int left,
        int right,
        const F& f
    ) const {
        assert(0 <= left && left <= right && right <= _n);
        if (left == right) return *this;
        return PersistentSegtreeBeats(
            _n,
            apply_node(_root, 0, _n, left, right, f),
            _pool
        );
    }

    PersistentSegtreeBeats copy_range_from(
        const PersistentSegtreeBeats& source,
        int left,
        int right
    ) const {
        assert(_n == source._n);
        assert(_pool == source._pool);
        assert(0 <= left && left <= right && right <= _n);
        if (left == right) return *this;
        return PersistentSegtreeBeats(
            _n,
            copy_range_node(
                _root,
                source._root,
                0,
                _n,
                left,
                right
            ),
            _pool
        );
    }

    std::vector<T> to_vector() const {
        return to_vector(0, _n);
    }

    std::vector<T> to_vector(int left, int right) const {
        assert(0 <= left && left <= right && right <= _n);
        std::vector<T> result;
        result.reserve(right - left);
        if (left != right) {
            collect_node(
                _root,
                0,
                _n,
                left,
                right,
                ActedMonoid::op_id(),
                result
            );
        }
        return result;
    }

    template <class Predicate>
    int max_right(int left, Predicate predicate) const {
        assert(0 <= left && left <= _n);
        assert(predicate(ActedMonoid::id()));
        if (left == _n) return _n;
        T product = ActedMonoid::id();
        return max_right_node(
            _root,
            0,
            _n,
            left,
            product,
            ActedMonoid::op_id(),
            predicate
        );
    }

    template <class Predicate>
    int min_left(int right, Predicate predicate) const {
        assert(0 <= right && right <= _n);
        assert(predicate(ActedMonoid::id()));
        if (right == 0) return 0;
        T product = ActedMonoid::id();
        return min_left_node(
            _root,
            0,
            _n,
            right,
            product,
            ActedMonoid::op_id(),
            predicate
        );
    }
};

}  // namespace ds
}  // namespace m1une

// END: ds/segtree/persistent_segtree_beats.hpp
#line 8 "..::sakumon::bonsai::reusable_lazy_segment_tree::main.cpp"

void solve() {
    int N, M;
    scan(N, M);
    vi A(N + 1);
    FORI(i, 1, N + 1) scan(A[i]);
    vi l(M + 1), r(M + 1), x(M + 1), L(M + 1), R(M + 1);
    FORI(i, 1, M + 1) scan(l[i]);
    FORI(i, 1, M + 1) scan(r[i]);
    FORI(i, 1, M + 1) scan(x[i]);
    FORI(i, 1, M + 1) scan(L[i]);
    FORI(i, 1, M + 1) scan(R[i]);

    using AM = m1une::beats_acted_monoid::RangeBitwiseAndOrRangeSum<u32>;
    using Seg = m1une::ds::PersistentSegtreeBeats<AM>;
    Seg seg(A);

    constexpr u32 msk = (1U << 30) - 1;

    int Q;
    scan(Q);
    FORI(i, 1, Q + 1) {
        int s, q;
        scan(s, q);
        int y = i;
        Seg cur = seg;
        FORI(j, 1, q + 1) {
            int z = (s + j) % M + 1;
            int u = min(N, max(1, l[z] ^ y));
            int v = min(N, max(1, r[z] ^ y));
            int U = min(N, max(1, L[z] ^ y));
            int V = min(N, max(1, R[z] ^ y));
            int l1 = min(u, v);
            int r1 = max(u, v);
            int L1 = min(U, V);
            int R1 = max(U, V);
            if (z % 2 == 0) {
                cur = cur.apply(l1, r1 + 1, AM::make_or(x[z] ^ y));
            } else {
                cur = cur.apply(l1, r1 + 1, AM::make_and(x[z] ^ y));
            }
            y = cur.prod(L1, R1 + 1).sum & msk;
        }
        print(y);
    }
}

int main() {
    CPP_DUMP_SET_OPTION(max_line_width, 80);
    CPP_DUMP_SET_OPTION(log_label_func, cpp_dump::log_label::filename());
    CPP_DUMP_SET_OPTION(enable_asterisk, true);
    int T = 1;
    // scan(T);
    while (T--) solve();
    return 0;
}
// END: ../sakumon/bonsai/reusable_lazy_segment_tree/main.cpp