// BEGIN: ../sakumon/bonsai/reusable_lazy_segment_tree/main2.cpp
#line 1 "..::sakumon::bonsai::reusable_lazy_segment_tree::main2.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::main2.cpp"

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

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

#include <array>
#include <limits>
#include <type_traits>

namespace m1une {
namespace acted_monoid {

template <typename T, int BITS>
struct RangeBitwiseAndOrXorRangeSumNode {
    T sum;
    std::array<long long, BITS> bit_count;
    long long size;
};

// Acted monoid for range bitwise AND, OR, and XOR updates and range sum queries.
template <typename T, int BITS = 30>
struct RangeBitwiseAndOrXorRangeSum {
    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 = RangeBitwiseAndOrXorRangeSumNode<T, BITS>;

    // Represents f(x) = (x & and_mask) ^ xor_mask on the lowest BITS bits.
    struct operator_type {
        T and_mask;
        T xor_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() {
        value_type res;
        res.sum = T(0);
        res.bit_count.fill(0);
        res.size = 0;
        return res;
    }

    static constexpr value_type op(const value_type& a, const value_type& b) {
        value_type res;
        res.sum = a.sum + b.sum;
        res.size = a.size + b.size;
        for (int i = 0; i < BITS; ++i) {
            res.bit_count[i] = a.bit_count[i] + b.bit_count[i];
        }
        return res;
    }

    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, (g.xor_mask & f.and_mask) ^ f.xor_mask};
    }

    static constexpr value_type mapping(const operator_type& f, const value_type& x) {
        value_type res = x;
        res.sum = T(0);
        for (int i = 0; i < BITS; ++i) {
            long long count = ((f.and_mask >> i) & T(1)) ? x.bit_count[i] : 0;
            if ((f.xor_mask >> i) & T(1)) count = x.size - count;
            res.bit_count[i] = count;
            res.sum += static_cast<T>(count) * (T(1) << i);
        }
        return res;
    }

    static constexpr value_type make(const T& value) {
        value_type res;
        res.sum = value;
        res.size = 1;
        for (int i = 0; i < BITS; ++i) {
            res.bit_count[i] = (value >> i) & T(1);
        }
        return res;
    }

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

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

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

}  // namespace acted_monoid
}  // namespace m1une

// END: acted_monoid/range_bitwise_and_or_xor_range_sum.hpp
#line 7 "..::sakumon::bonsai::reusable_lazy_segment_tree::main2.cpp"
// BEGIN: ds/segtree/rollback_lazy_segtree.hpp
#line 3 "ds::segtree::rollback_lazy_segtree.hpp"

#include <bit>
#include <cassert>
#include <concepts>
#include <utility>
#include <vector>

// 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 11 "ds::segtree::rollback_lazy_segtree.hpp"
// BEGIN: ../../math/bit_ceil.hpp
#line 3 "..::..::math::bit_ceil.hpp"

namespace m1une {
namespace math {

template <typename T>
constexpr T bit_ceil(T n) {
    if (n <= 1) return 1;
    T x = 1;
    while (x < n) x <<= 1;
    return x;
}

}  // namespace math
}  // namespace m1une

// END: ../../math/bit_ceil.hpp
#line 12 "ds::segtree::rollback_lazy_segtree.hpp"
// BEGIN: ../detail/rollback_journal.hpp
#line 3 "..::detail::rollback_journal.hpp"

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

namespace m1une {
namespace ds {
namespace detail {

template <class Node>
struct RollbackJournal {
    struct Change {
        int index;
        Node value;
    };

    struct Checkpoint {
        std::size_t change_size;
        std::size_t node_size;
        std::uint64_t epoch;
    };

    std::vector<Node> nodes;
    std::vector<Change> changes;
    std::vector<Checkpoint> checkpoints;
    std::vector<std::uint64_t> saved_epoch;
    std::uint64_t next_epoch = 1;

    std::uint64_t new_epoch() {
        if (next_epoch == 0) {
            std::fill(saved_epoch.begin(), saved_epoch.end(), 0);
            next_epoch = 1;
        }
        return next_epoch++;
    }

    int size() const { return int(nodes.size()); }

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

    template <class... Args>
    int emplace(Args&&... args) {
        assert(nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        int index = int(nodes.size());
        nodes.emplace_back(std::forward<Args>(args)...);
        saved_epoch.push_back(0);
        return index;
    }

    int snapshot() {
        assert(checkpoints.size() < std::size_t(std::numeric_limits<int>::max()));
        checkpoints.push_back(Checkpoint{changes.size(), nodes.size(), new_epoch()});
        return int(checkpoints.size());
    }

    void touch(int index) {
        assert(0 <= index && index < size());
        if (checkpoints.empty()) return;
        const Checkpoint& checkpoint = checkpoints.back();
        if (std::size_t(index) >= checkpoint.node_size) return;
        if (saved_epoch[index] == checkpoint.epoch) return;
        saved_epoch[index] = checkpoint.epoch;
        changes.push_back(Change{index, nodes[index]});
    }

    int snapshot_count() const { return int(checkpoints.size()); }

    void reserve_snapshots(int count) {
        assert(0 <= count);
        checkpoints.reserve(count);
    }

    void reserve_changes(std::size_t count) { changes.reserve(count); }

    void rollback(int state) {
        assert(1 <= state && state <= snapshot_count());
        Checkpoint checkpoint = checkpoints[state - 1];
        while (changes.size() > checkpoint.change_size) {
            Change change = std::move(changes.back());
            changes.pop_back();
            nodes[change.index] = std::move(change.value);
        }
        nodes.erase(nodes.begin() + checkpoint.node_size, nodes.end());
        saved_epoch.resize(checkpoint.node_size);
        checkpoints.resize(state);
        checkpoints.back().change_size = changes.size();
        checkpoints.back().node_size = nodes.size();
        checkpoints.back().epoch = new_epoch();
    }

    void clear_history() {
        changes.clear();
        checkpoints.clear();
        std::fill(saved_epoch.begin(), saved_epoch.end(), 0);
    }

    void clear() {
        nodes.clear();
        changes.clear();
        checkpoints.clear();
        saved_epoch.clear();
        next_epoch = 1;
    }
};

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

// END: ../detail/rollback_journal.hpp
#line 13 "ds::segtree::rollback_lazy_segtree.hpp"

namespace m1une {
namespace ds {

template <m1une::acted_monoid::IsActedMonoid ActedMonoid>
struct RollbackLazySegtree {
    using T = typename ActedMonoid::value_type;
    using F = typename ActedMonoid::operator_type;

   private:
    struct Node {
        T value = ActedMonoid::id();
        F lazy = ActedMonoid::op_id();
        bool has_lazy = false;
    };

    int _n = 0;
    int _size = 1;
    int _log = 0;
    detail::RollbackJournal<Node> _journal;

    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 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;
        }
    }

    template <class 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);
        }
    }

    int node_length(int node) const {
        int level = std::bit_width(static_cast<unsigned int>(node)) - 1;
        return _size >> level;
    }

    int node_left(int node) const {
        int level = std::bit_width(static_cast<unsigned int>(node)) - 1;
        int length = _size >> level;
        return (node - (1 << level)) * length;
    }

    void update(int node) {
        _journal.touch(node);
        _journal[node].value = ActedMonoid::op(
            _journal[node << 1].value,
            _journal[node << 1 | 1].value
        );
    }

    void all_apply(int node, const F& f) {
        _journal.touch(node);
        _journal[node].value = mapping_at(f, _journal[node].value, 0);
        if (node < _size) {
            _journal[node].lazy = ActedMonoid::op_comp(f, _journal[node].lazy);
            _journal[node].has_lazy = true;
        }
    }

    void push(int node) {
        if (!_journal[node].has_lazy) return;
        F lazy = _journal[node].lazy;
        all_apply(node << 1, lazy);
        all_apply(node << 1 | 1, shift_operator(lazy, node_length(node) / 2));
        _journal.touch(node);
        _journal[node].lazy = ActedMonoid::op_id();
        _journal[node].has_lazy = false;
    }

    template <class U>
    void build(const std::vector<U>& values) {
        _n = int(values.size());
        _size = int(m1une::math::bit_ceil(static_cast<unsigned int>(_n)));
        _log = 0;
        while ((1U << _log) < static_cast<unsigned int>(_size)) ++_log;
        _journal.nodes.assign(2 * _size, Node());
        _journal.saved_epoch.assign(_journal.nodes.size(), 0);
        for (int index = 0; index < _n; ++index) {
            _journal[_size + index].value = make_value(values[index], index);
        }
        for (int node = _size - 1; node > 0; --node) {
            _journal[node].value = ActedMonoid::op(
                _journal[node << 1].value,
                _journal[node << 1 | 1].value
            );
        }
    }

   public:
    RollbackLazySegtree() { build(std::vector<T>()); }
    explicit RollbackLazySegtree(int n) {
        assert(0 <= n);
        build(std::vector<T>(n, ActedMonoid::id()));
    }
    explicit RollbackLazySegtree(const std::vector<T>& values) { build(values); }
    explicit RollbackLazySegtree(std::vector<T>&& values) { build(values); }

    template <class U>
        requires(!std::same_as<U, T>)
    explicit RollbackLazySegtree(const std::vector<U>& values) { build(values); }

    int size() const { return _n; }
    bool empty() const { return _n == 0; }
    std::size_t node_count() const { return _journal.nodes.size(); }

    void set(int pos, T value) {
        assert(0 <= pos && pos < _n);
        int node = pos + _size;
        for (int level = _log; level >= 1; --level) push(node >> level);
        _journal.touch(node);
        _journal[node].value = std::move(value);
        for (int level = 1; level <= _log; ++level) update(node >> level);
    }

    void set_inplace(int pos, T value) { set(pos, std::move(value)); }

    T get(int pos) {
        assert(0 <= pos && pos < _n);
        int node = pos + _size;
        for (int level = _log; level >= 1; --level) push(node >> level);
        return _journal[node].value;
    }

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

    T prod(int left, int right) {
        assert(0 <= left && left <= right && right <= _n);
        if (left == right) return ActedMonoid::id();
        left += _size;
        right += _size;
        for (int level = _log; level >= 1; --level) {
            if (((left >> level) << level) != left) push(left >> level);
            if (((right >> level) << level) != right) push((right - 1) >> level);
        }
        T left_product = ActedMonoid::id();
        T right_product = ActedMonoid::id();
        while (left < right) {
            if (left & 1) left_product = ActedMonoid::op(left_product, _journal[left++].value);
            if (right & 1) right_product = ActedMonoid::op(_journal[--right].value, right_product);
            left >>= 1;
            right >>= 1;
        }
        return ActedMonoid::op(left_product, right_product);
    }

    T all_prod() const { return _journal[1].value; }

    std::vector<T> to_vector() {
        for (int node = 1; node < _size; ++node) push(node);
        std::vector<T> result;
        result.reserve(_n);
        for (int index = 0; index < _n; ++index) result.push_back(_journal[_size + index].value);
        return result;
    }

    std::vector<T> to_vector(int left, int right) {
        assert(0 <= left && left <= right && right <= _n);
        std::vector<T> result;
        result.reserve(right - left);
        for (int index = left; index < right; ++index) result.push_back(get(index));
        return result;
    }

    void apply(int pos, const F& f) {
        assert(0 <= pos && pos < _n);
        int node = pos + _size;
        for (int level = _log; level >= 1; --level) push(node >> level);
        _journal.touch(node);
        _journal[node].value = mapping_at(f, _journal[node].value, 0);
        for (int level = 1; level <= _log; ++level) update(node >> level);
    }

    void apply(int left, int right, const F& f) {
        assert(0 <= left && left <= right && right <= _n);
        if (left == right) return;
        int base_left = left;
        left += _size;
        right += _size;
        for (int level = _log; level >= 1; --level) {
            if (((left >> level) << level) != left) push(left >> level);
            if (((right >> level) << level) != right) push((right - 1) >> level);
        }
        int saved_left = left;
        int saved_right = right;
        while (left < right) {
            if (left & 1) {
                all_apply(left, shift_operator(f, node_left(left) - base_left));
                ++left;
            }
            if (right & 1) {
                --right;
                all_apply(right, shift_operator(f, node_left(right) - base_left));
            }
            left >>= 1;
            right >>= 1;
        }
        left = saved_left;
        right = saved_right;
        for (int level = 1; level <= _log; ++level) {
            if (((left >> level) << level) != left) update(left >> level);
            if (((right >> level) << level) != right) update((right - 1) >> level);
        }
    }

    void apply_inplace(int pos, const F& f) { apply(pos, f); }
    void apply_inplace(int left, int right, const F& f) { apply(left, right, f); }

    template <class Predicate>
    int max_right(int left, Predicate predicate) {
        assert(0 <= left && left <= _n);
        assert(predicate(ActedMonoid::id()));
        if (left == _n) return _n;
        int node = left + _size;
        for (int level = _log; level >= 1; --level) push(node >> level);
        T product = ActedMonoid::id();
        do {
            while ((node & 1) == 0) node >>= 1;
            T next = ActedMonoid::op(product, _journal[node].value);
            if (!predicate(next)) {
                while (node < _size) {
                    push(node);
                    node <<= 1;
                    next = ActedMonoid::op(product, _journal[node].value);
                    if (predicate(next)) {
                        product = std::move(next);
                        ++node;
                    }
                }
                return node - _size;
            }
            product = std::move(next);
            ++node;
        } while ((node & -node) != node);
        return _n;
    }

    template <class Predicate>
    int min_left(int right, Predicate predicate) {
        assert(0 <= right && right <= _n);
        assert(predicate(ActedMonoid::id()));
        if (right == 0) return 0;
        int node = right + _size;
        for (int level = _log; level >= 1; --level) push((node - 1) >> level);
        T product = ActedMonoid::id();
        do {
            --node;
            while (node > 1 && (node & 1)) node >>= 1;
            T next = ActedMonoid::op(_journal[node].value, product);
            if (!predicate(next)) {
                while (node < _size) {
                    push(node);
                    node = node << 1 | 1;
                    next = ActedMonoid::op(_journal[node].value, product);
                    if (predicate(next)) {
                        product = std::move(next);
                        --node;
                    }
                }
                return node + 1 - _size;
            }
            product = std::move(next);
        } while ((node & -node) != node);
        return 0;
    }

    int snapshot() { return _journal.snapshot(); }
    int snapshot_count() const { return _journal.snapshot_count(); }
    void reserve_snapshots(int count) { _journal.reserve_snapshots(count); }
    void rollback(int state) { _journal.rollback(state); }
    void clear_history() { _journal.clear_history(); }
    void release() { _n = 0; _size = 1; _log = 0; _journal.clear(); }
};

}  // namespace ds
}  // namespace m1une

// END: ds/segtree/rollback_lazy_segtree.hpp
#line 8 "..::sakumon::bonsai::reusable_lazy_segment_tree::main2.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::acted_monoid::RangeBitwiseAndOrXorRangeSum<u32>;
    using Seg = m1une::ds::RollbackLazySegtree<AM>;
    Seg seg(A);
    int state = seg.snapshot();

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

    int Q;
    scan(Q);
    FORI(i, 1, Q + 1) {
        if (i > 1) seg.rollback(state);
        int s, q;
        scan(s, q);
        int y = i;
        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) {
                seg.apply_inplace(l1, r1 + 1, AM::make_or(x[z] ^ y));
            } else {
                seg.apply_inplace(l1, r1 + 1, AM::make_and(x[z] ^ y));
            }
            y = seg.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/main2.cpp