#include <bits/stdc++.h>

#ifdef _MSC_VER
#  include <intrin.h>
#else
#  include <x86intrin.h>
#endif

#include <limits>
#include <type_traits>

namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
    if constexpr (cond_v) {
        return std::forward<Then>(then);
    } else {
        return std::forward<OrElse>(or_else);
    }
}

// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;

template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;

// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;

// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long int> { using type = __uint128_t; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;

template <typename T, typename = void>
struct rec_value_type {
    using type = T;
};
template <typename T>
struct rec_value_type<T, std::void_t<typename T::value_type>> {
    using type = typename rec_value_type<typename T::value_type>::type;
};
template <typename T>
using rec_value_type_t = typename rec_value_type<T>::type;

} // namespace suisen

// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;

// ! macros (internal)
#define DETAIL_OVERLOAD2(_1,_2,name,...) name
#define DETAIL_OVERLOAD3(_1,_2,_3,name,...) name
#define DETAIL_OVERLOAD4(_1,_2,_3,_4,name,...) name

#define DETAIL_REP4(i,l,r,s)  for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define DETAIL_REP3(i,l,r)    DETAIL_REP4(i,l,r,1)
#define DETAIL_REP2(i,n)      DETAIL_REP3(i,0,n)
#define DETAIL_REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define DETAIL_REPINF2(i,l)   DETAIL_REPINF3(i,l,1)
#define DETAIL_REPINF1(i)     DETAIL_REPINF2(i,0)
#define DETAIL_RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define DETAIL_RREP3(i,l,r)   DETAIL_RREP4(i,l,r,1)
#define DETAIL_RREP2(i,n)     DETAIL_RREP3(i,0,n)

#define DETAIL_CAT_I(a, b) a##b
#define DETAIL_CAT(a, b) DETAIL_CAT_I(a, b)
#define DETAIL_UNIQVAR(tag) DETAIL_CAT(tag, __LINE__)

// ! macros
#define REP(...)    DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_REP4   , DETAIL_REP3   , DETAIL_REP2   )(__VA_ARGS__)
#define RREP(...)   DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_RREP4  , DETAIL_RREP3  , DETAIL_RREP2  )(__VA_ARGS__)
#define REPINF(...) DETAIL_OVERLOAD3(__VA_ARGS__, DETAIL_REPINF3, DETAIL_REPINF2, DETAIL_REPINF1)(__VA_ARGS__)

#define LOOP(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> DETAIL_UNIQVAR(loop_variable) = n; DETAIL_UNIQVAR(loop_variable) --> 0;)

#define ALL(iterable) std::begin(iterable), std::end(iterable)
#define INPUT(type, ...) type __VA_ARGS__; read(__VA_ARGS__)

// ! debug

#ifdef LOCAL
#  define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__)

template <class T, class... Args>
void debug_internal(const char* s, T&& first, Args&&... args) {
    constexpr const char* prefix = "[\033[32mDEBUG\033[m] ";
    constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "(";
    constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")";
    std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward<T>(first);
    ((std::cerr << ", " << std::forward<Args>(args)), ...);
    std::cerr << close_brakets << "\n";
}

#else
#  define debug(...) void(0)
#endif

// ! I/O utilities

// __int128_t
std::ostream& operator<<(std::ostream& dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}
// __uint128_t
std::ostream& operator<<(std::ostream& dest, __uint128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[value % 10];
            value /= 10;
        } while (value != 0);
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}

// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U>& a) {
    return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...>& a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return out;
    else {
        out << std::get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) out << ' ';
        return operator<<<N + 1>(out, a);
    }
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T>& a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N>& a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head& head, const Tail &...tails) {
    std::cout << head;
    if (sizeof...(tails)) std::cout << ' ';
    print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
    for (auto it = v.begin(); it != v.end();) {
        std::cout << *it;
        if (++it != v.end()) std::cout << sep;
    }
    std::cout << end;
}

__int128_t stoi128(const std::string& s) {
    __int128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    if (s[0] == '-') ret = -ret;
    return ret;
}
__uint128_t stou128(const std::string& s) {
    __uint128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    return ret;
}
// __int128_t
std::istream& operator>>(std::istream& in, __int128_t& v) {
    std::string s;
    in >> s;
    v = stoi128(s);
    return in;
}
// __uint128_t
std::istream& operator>>(std::istream& in, __uint128_t& v) {
    std::string s;
    in >> s;
    v = stou128(s);
    return in;
}
// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U>& a) {
    return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...>& a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return in;
    else return operator>><N + 1>(in >> std::get<N>(a), a);
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T>& a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N>& a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
template <typename ...Args>
void read(Args &...args) {
    (std::cin >> ... >> args);
}

// ! integral utilities

// Returns pow(-1, n)
template <typename T> constexpr inline int pow_m1(T n) {
    return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <> constexpr inline int pow_m1<bool>(bool n) {
    return -int(n) | 1;
}

// Returns floor(x / y)
template <typename T> constexpr inline T fld(const T x, const T y) {
    return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T> constexpr inline T cld(const T x, const T y) {
    return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}

template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); }
template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T> constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T> constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }
template <typename T> constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T> constexpr inline int parity(const T x) { return popcount(x) & 1; }

// ! container

template <typename T, typename Comparator>
auto priqueue_comp(const Comparator comparator) {
    return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}

template <typename Container>
void sort_unique_erase(Container& a) {
    std::sort(a.begin(), a.end());
    a.erase(std::unique(a.begin(), a.end()), a.end());
}

template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
    if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container &&c, BiConsumer f) -> decltype(c.begin(), c.end(), void()) {
    foreach_adjacent_values(c.begin(), c.end(), f);
}

// ! other utilities

// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T& x, const T& y) {
    return y >= x ? false : (x = y, true);
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T& x, const T& y) {
    return y <= x ? false : (x = y, true);
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::string bin(T val, int bit_num = -1) {
    std::string res;
    if (bit_num != -1) {
        for (int bit = bit_num; bit-- > 0;) res += '0' + ((val >> bit) & 1);
    } else {
        for (; val; val >>= 1) res += '0' + (val & 1);
        std::reverse(res.begin(), res.end());
    }
    return res;
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_low_to_high(T val, T base = 10) {
    std::vector<T> res;
    for (; val; val /= base) res.push_back(val % base);
    if (res.empty()) res.push_back(T{ 0 });
    return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_high_to_low(T val, T base = 10) {
    auto res = digits_low_to_high(val, base);
    std::reverse(res.begin(), res.end());
    return res;
}

template <typename T>
std::string join(const std::vector<T>& v, const std::string& sep, const std::string& end) {
    std::ostringstream ss;
    for (auto it = v.begin(); it != v.end();) {
        ss << *it;
        if (++it != v.end()) ss << sep;
    }
    ss << end;
    return ss.str();
}

template <typename Func, typename Seq>
auto transform_to_vector(const Func &f, const Seq &s) {
    std::vector<std::invoke_result_t<Func, typename Seq::value_type>> v;
    v.reserve(std::size(s)), std::transform(std::begin(s), std::end(s), std::back_inserter(v), f);
    return v;
}
template <typename T, typename Seq>
auto copy_to_vector(const Seq &s) {
    std::vector<T> v;
    v.reserve(std::size(s)), std::copy(std::begin(s), std::end(s), std::back_inserter(v));
    return v;
}
template <typename Seq>
Seq concat(Seq s, const Seq &t) {
    s.reserve(std::size(s) + std::size(t));
    std::copy(std::begin(t), std::end(t), std::back_inserter(s));
    return s;
}
template <typename Seq>
std::vector<Seq> split(const Seq s, typename Seq::value_type delim) {
    std::vector<Seq> res;
    for (auto itl = std::begin(s), itr = itl;; itl = ++itr) {
        while (itr != std::end(s) and *itr != delim) ++itr;
        res.emplace_back(itl, itr);
        if (itr == std::end(s)) return res;
    }
}

int digit_to_int(char c) { return c - '0'; }
int lowercase_to_int(char c) { return c - 'a'; }
int uppercase_to_int(char c) { return c - 'A'; }

std::vector<int> digit_str_to_ints(const std::string &s) {
    return transform_to_vector(digit_to_int, s);
}
std::vector<int> lowercase_str_to_ints(const std::string &s) {
    return transform_to_vector(lowercase_to_int, s);
}
std::vector<int> uppercase_str_to_ints(const std::string &s) {
    return transform_to_vector(uppercase_to_int, s);
}

const std::string Yes = "Yes", No = "No", YES = "YES", NO = "NO";

namespace suisen {}
using namespace suisen;
using namespace std;

struct io_setup {
    io_setup(int precision = 20) {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(precision);
    }
} io_setup_ {};

// ! code from here

#include <atcoder/modint>

using mint = atcoder::modint998244353;

namespace atcoder {
    std::istream& operator>>(std::istream& in, mint& a) {
        long long e; in >> e; a = e;
        return in;
    }

    std::ostream& operator<<(std::ostream& out, const mint& a) {
        out << a.val();
        return out;
    }
} // namespace atcoder

#include <iostream>
#include <utility>

namespace suisen {
    template <typename T>
    struct Affine {
        T a, b;
        Affine(const T &a = 1, const T &b = 0) : a(a), b(b) {}

        static Affine<T> id() { return Affine<T>{}; }
        static Affine<T> compose(const Affine<T>& f, const Affine<T>& g) { return f.compose(g); }

        Affine<T> compose(const Affine<T>& g) const { return { a * g.a, affine(g.b) }; }

        template <typename U = T>
        U affine(const T &x) const { return U(a) * x + b; }
        T operator()(const T &x) const { return affine<T>(x); }

        Affine<T> operator+() const { return *this; }
        Affine<T> operator-() const { return { -a, -b }; }

        Affine<T>& operator++() { ++b; return *this; }
        Affine<T>& operator--() { --b; return *this; }
        Affine<T> operator++(int) { Affine<T> f(*this); ++(*this); return f; }
        Affine<T> operator--(int) { Affine<T> f(*this); --(*this); return f; }

        Affine<T>& operator+=(const T& c) { b += c; return *this; }
        Affine<T>& operator-=(const T& c) { b -= c; return *this; }
        friend Affine<T> operator+(Affine<T> f, const T &c) { f += c; return f; }
        friend Affine<T> operator-(Affine<T> f, const T &c) { f -= c; return f; }

        Affine<T>& operator+=(const Affine<T> &g) { a += g.a, b += g.b; return *this; }
        Affine<T>& operator-=(const Affine<T> &g) { a -= g.a, b -= g.b; return *this; }
        friend Affine<T> operator+(Affine<T> f, const Affine<T> &g) { f += g; return f; }
        friend Affine<T> operator-(Affine<T> f, const Affine<T> &g) { f -= g; return f; }

        friend bool operator==(const Affine<T> &f, const Affine<T> &g) { return f.a == g.a and f.b == g.b; }
        friend bool operator!=(const Affine<T> &f, const Affine<T> &g) { return not (f == g); }
        friend bool operator< (const Affine<T> &f, const Affine<T> &g) { return f.a < g.a or (f.a == g.a and f.b < g.b); }
        friend bool operator<=(const Affine<T> &f, const Affine<T> &g) { return not (g < f); }
        friend bool operator> (const Affine<T> &f, const Affine<T> &g) { return g < f; }
        friend bool operator>=(const Affine<T> &f, const Affine<T> &g) { return not (f < g); }

        template <typename U = T, typename V = T>
        operator std::pair<U, V>() { return std::pair<U, V>{ a, b }; }
        template <typename U = T, typename V = T>
        operator std::tuple<U, V>() { return std::tuple<U, V>{ a, b }; }

        friend std::istream& operator<<(std::istream& in, Affine<T> &f) { return in >> f.a >> f.b; }
        friend std::ostream& operator>>(std::ostream& out, const Affine<T> &f) { return out << f.a << ' ' << f.b; }
    };
} // namespace suisen

#include <cassert>
#include <vector>

namespace suisen {
    template <typename T, typename F, T(*mapping)(F, T), F(*composition)(F, F), F(*id)()>
    struct CommutativeDualSegmentTree {
        CommutativeDualSegmentTree() {}
        CommutativeDualSegmentTree(std::vector<T>&& a) : n(a.size()), m(ceil_pow2(a.size())), data(std::move(a)), lazy(m, id()) {}
        CommutativeDualSegmentTree(const std::vector<T>& a) : CommutativeDualSegmentTree(std::vector<T>(a)) {}
        CommutativeDualSegmentTree(int n, const T& fill_value) : CommutativeDualSegmentTree(std::vector<T>(n, fill_value)) {}

        T operator[](int i) const {
            assert(0 <= i and i < n);
            T res = data[i];
            for (i = (i + m) >> 1; i; i >>= 1) res = mapping(lazy[i], res);
            return res;
        }
        T get(int i) const {
            return (*this)[i];
        }
        void apply(int l, int r, const F& f) {
            assert(0 <= l and r <= n);
            for (l += m, r += m; l < r; l >>= 1, r >>= 1) {
                if (l & 1) apply(l++, f);
                if (r & 1) apply(--r, f);
            }
        }
    protected:
        int n, m;
        std::vector<T> data;
        std::vector<F> lazy;

        void apply(int k, const F& f) {
            if (k < m) {
                lazy[k] = composition(f, lazy[k]);
            } else if (k - m < n) {
                data[k - m] = mapping(f, data[k - m]);
            }
        }
    private:
        static int ceil_pow2(int n) {
            int m = 1;
            while (m < n) m <<= 1;
            return m;
        }
    };
} // namespace suisen

namespace suisen {
    template <typename T, typename F, T(*mapping)(F, T), F(*composition)(F, F), F(*id)()>
    struct DualSegmentTree : public CommutativeDualSegmentTree<T, F, mapping, composition, id> {
        using base_type = CommutativeDualSegmentTree<T, F, mapping, composition, id>;
        using base_type::base_type;
        void apply(int l, int r, const F& f) {
            push(l, r);
            base_type::apply(l, r, f);
        }
    private:
        void push(int k) {
            base_type::apply(2 * k, this->lazy[k]), base_type::apply(2 * k + 1, this->lazy[k]);
            this->lazy[k] = id();
        }
        void push(int l, int r) {
            const int log = __builtin_ctz(this->m);

            l += this->m, r += this->m;

            for (int i = log; i >= 1; i--) {
                if (((l >> i) << i) != l) push(l >> i);
                if (((r >> i) << i) != r) push((r - 1) >> i);
            }
        }
    };

    template <typename T, typename F, T(*mapping)(F, T), F(*composition)(F, F), F(*id)()>
    DualSegmentTree(int, T)->DualSegmentTree<T, F, mapping, composition, id>;

    template <typename T, typename F, T(*mapping)(F, T), F(*composition)(F, F), F(*id)()>
    DualSegmentTree(std::vector<T>)->DualSegmentTree<T, F, mapping, composition, id>;
} // namespace suisen

using S = mint;
using F = Affine<mint>;

S mapping(F f, S x) {
    return f(x);
}
F composition(F f, F g) {
    return Affine<mint>::compose(f, g);
}
F id() {
    return Affine<mint>::id();
}

namespace suisen {
class HeavyLightDecomposition {
    public:
        template <typename Q>
        using is_point_update_query = std::is_invocable<Q, int>;
        template <typename Q>
        using is_range_update_query = std::is_invocable<Q, int, int>;
        template <typename Q, typename T>
        using is_point_get_query  = std::is_same<std::invoke_result_t<Q, int>, T>;
        template <typename Q, typename T>
        using is_range_fold_query = std::is_same<std::invoke_result_t<Q, int, int>, T>;

        using Graph = std::vector<std::vector<int>>;

        HeavyLightDecomposition() = default;
        HeavyLightDecomposition(Graph &g) : n(g.size()), visit(n), leave(n), head(n), ord(n), siz(n), par(n, -1), dep(n, 0) {
            for (int i = 0; i < n; ++i) if (par[i] < 0) dfs(g, i, -1);
            int time = 0;
            for (int i = 0; i < n; ++i) if (par[i] < 0) hld(g, i, -1, time);
        }
        int size() const {
            return n;
        }
        int lca(int u, int v) const {
            for (;; v = par[head[v]]) {
                if (visit[u] > visit[v]) std::swap(u, v);
                if (head[u] == head[v]) return u;
            }
        }
        int la(int u, int k, int default_value = -1) const {
            if (k < 0) return default_value;
            while (u >= 0) {
                int h = head[u];
                if (visit[u] - k >= visit[h]) return ord[visit[u] - k];
                k -= visit[u] - visit[h] + 1;
                u = par[h];
            }
            return default_value;
        }
        int jump(int u, int v, int d, int default_value = -1) const {
            if (d < 0) return default_value;
            const int w = lca(u, v);
            int uw = dep[u] - dep[w];
            if (d <= uw) return la(u, d);
            int vw = dep[v] - dep[w];
            return d <= uw + vw ? la(v, (uw + vw) - d) : default_value;
        }
        int dist(int u, int v) const {
            return dep[u] + dep[v] - 2 * dep[lca(u, v)];
        }
        template <typename T, typename Q, typename F, constraints_t<is_range_fold_query<Q, T>, is_bin_op<F, T>> = nullptr>
        T fold_path(int u, int v, T identity, F bin_op, Q fold_query, bool is_edge_query = false) const {
            T res = identity;
            for (;; v = par[head[v]]) {
                if (visit[u] > visit[v]) std::swap(u, v);
                if (head[u] == head[v]) break;
                res = bin_op(fold_query(visit[head[v]], visit[v] + 1), res);
            }
            return bin_op(fold_query(visit[u] + is_edge_query, visit[v] + 1), res);
        }
        template <
            typename T, typename Q1, typename Q2, typename F,
            constraints_t<is_range_fold_query<Q1, T>, is_range_fold_query<Q2, T>, is_bin_op<F, T>> = nullptr
        >
        T fold_path_noncommutative(int u, int v, T identity, F bin_op, Q1 fold_query, Q2 fold_query_rev, bool is_edge_query = false) const {
            T res_u = identity, res_v = identity;
            // a := lca(u, v)
            // res = fold(u -> a) + fold(a -> v)
            while (head[u] != head[v]) {
                if (visit[u] < visit[v]) { // a -> v
                    res_v = bin_op(fold_query(visit[head[v]], visit[v] + 1), res_v);
                    v = par[head[v]];
                } else { // u -> a
                    res_u = bin_op(res_u, fold_query_rev(visit[head[u]], visit[u] + 1));
                    u = par[head[u]];
                }
            }
            if (visit[u] < visit[v]) { // a = u
                res_v = bin_op(fold_query(visit[u] + is_edge_query, visit[v] + 1), res_v);
            } else { // a = v
                res_u = bin_op(res_u, fold_query_rev(visit[v] + is_edge_query, visit[u] + 1));
            }
            return bin_op(res_u, res_v);
        }
        template <typename Q, constraints_t<is_range_update_query<Q>> = nullptr>
        void update_path(int u, int v, Q update_query, bool is_edge_query = false) const {
            for (;; v = par[head[v]]) {
                if (visit[u] > visit[v]) std::swap(u, v);
                if (head[u] == head[v]) break;
                update_query(visit[head[v]], visit[v] + 1);
            }
            update_query(visit[u] + is_edge_query, visit[v] + 1);
        }
        template <typename T, typename Q, constraints_t<is_range_fold_query<Q, T>> = nullptr>
        T fold_subtree(int u, Q fold_query, bool is_edge_query = false) const {
            return fold_query(visit[u] + is_edge_query, leave[u]);
        }
        template <typename Q, constraints_t<is_range_update_query<Q>> = nullptr>
        void update_subtree(int u, Q update_query, bool is_edge_query = false) const {
            update_query(visit[u] + is_edge_query, leave[u]);
        }
        template <typename T, typename Q, constraints_t<is_point_get_query<Q, T>> = nullptr>
        T get_point(int u, Q get_query) const {
            return get_query(visit[u]);
        }
        template <typename Q, constraints_t<is_point_update_query<Q>> = nullptr>
        void update_point(int u, Q update_query) const {
            update_query(visit[u]);
        }
        std::vector<int> inv_ids() const {
            std::vector<int> inv(n);
            for (int i = 0; i < n; ++i) inv[visit[i]] = i;
            return inv;
        }
        int get_visit_time(int u) const {
            return visit[u];
        }
        int get_leave_time(int u) const {
            return leave[u];
        }
        int get_head(int u) const {
            return head[u];
        }
        int get_kth_visited(int k) const {
            return ord[k];
        }
        int get_subtree_size(int u) const {
            return siz[u];
        }
        int get_parent(int u) const {
            return par[u];
        }
        int get_depth(int u) const {
            return dep[u];
        }
        std::vector<int> get_roots() const {
            std::vector<int> res;
            for (int i = 0; i < n; ++i) if (par[i] < 0) res.push_back(i);
            return res;
        }
    private:
        int n;
        std::vector<int> visit, leave, head, ord, siz, par, dep;
        int dfs(Graph &g, int u, int p) {
            par[u] = p;
            siz[u] = 1;
            int max_size = 0;
            for (int &v : g[u]) {
                if (v == p) continue;
                dep[v] = dep[u] + 1;
                siz[u] += dfs(g, v, u);
                if (max_size < siz[v]) {
                    max_size = siz[v];
                    std::swap(g[u].front(), v);
                }
            }
            return siz[u];
        }
        void hld(Graph &g, int u, int p, int &time) {
            visit[u] = time, ord[time] = u, ++time;
            head[u] = p >= 0 and g[p].front() == u ? head[p] : u;
            for (int v : g[u]) {
                if (v != p) hld(g, v, u, time);
            }
            leave[u] = time;
        }
};
} // namespace suisen

int main() {
    int n, q;
    read(n, q);

    vector<vector<int>> g(n);
    LOOP(n - 1) {
        int u, v;
        read(u, v);
        --u, --v;
        g[u].push_back(v);
        g[v].push_back(u);
    }
    HeavyLightDecomposition hld(g);
    vector<int> inv_ids = hld.inv_ids();

    vector<mint> x(n);
    read(x);

    vector<int> par(n, -1);
    {
        auto dfs = [&](auto dfs, int u) -> void {
            for (int v : g[u]) {
                par[v] = u;
                g[v].erase(find(ALL(g[v]), u));
                dfs(dfs, v);
            }
        };
        dfs(dfs, 0);
    }

    const int B = ::sqrt(n);

    auto is_large = [&](int i) {
        return int(g[i].size()) >= B;
    };

    vector<int> idx(n);
    vector<int> vs1, vs2;

    vector<int8_t> mark(n, false);
    vector<int> from(n, -1);
    {
        int num = 0;
        REP(i, n) if (is_large(i)) {
            from[i] = num;
            for (int j : g[i]) {
                mark[j] = true;
                idx[j] = vs1.size();
                vs1.push_back(j);
            }
            num += g[i].size();
        }
    }

    vector<int> mark_cnt(n);
    vector<int> mark_vs;

    vector<int> ll(n), lr(n), sl(n), sr(n);
    vector<int> lvs;
    {
        auto dfs = [&](auto dfs, int u) -> void {
            mark_cnt[u] = mark_vs.size();

            ll[u] = lvs.size();
            sl[u] = vs2.size();
            if (not mark[u]) {
                idx[u] = vs2.size();
                vs2.push_back(u);
            } else {
                mark_vs.push_back(u);
            }
            if (is_large(u)) {
                lvs.push_back(u);
            }
            for (int v : g[u]) dfs(dfs, v);
            lr[u] = lvs.size();
            sr[u] = vs2.size();
        };
        dfs(dfs, 0);
    }

    vector<mint> d1, d2;
    for (int v : vs1) d1.push_back(x[v]);
    for (int v : vs2) d2.push_back(x[v]);

    DualSegmentTree<mint, F, mapping, composition, id> seg1(d1), seg2(d2);

    LOOP(q) {
        int qt;
        read(qt);
        if (qt == 1) {
            int v;
            read(v);
            --v;
            if (mark[v]) {
                print(seg1.get(idx[v]));
            } else {
                print(seg2.get(idx[v]));
            }
        } else if (qt == 2) {
            int v, k;
            mint c, d;
            read(v, k, c, d);
            --v;

            for (int x : { par[v], v }) if (x != -1) {
                if (mark[x]) {
                    seg1.apply(idx[x], idx[x] + 1, { c, d });
                } else {
                    seg2.apply(idx[x], idx[x] + 1, { c, d });
                }
            }

            if (is_large(v)) {
                seg1.apply(from[v], from[v] + int(g[v].size()), { c, d });
            } else {
                for (int x : g[v]) {
                    seg2.apply(idx[x], idx[x] + 1, { c, d });
                }
            }
        } else if (qt == 3) {
            int v;
            mint c, d;
            read(v, c, d);
            --v;
            seg2.apply(sl[v], sr[v], { c, d });
            REP(i, ll[v], lr[v]) {
                int x = lvs[i];
                seg1.apply(from[x], from[x] + int(g[x].size()), { c, d });
            }
            if (mark[v]) {
                seg1.apply(idx[v], idx[v] + 1, { c, d });
            }
        } else {
            int u, v;
            mint c, d;
            read(u, v, c, d);
            --u, --v;

            hld.update_path(u, v, [&](int l, int r) {
                int off_l = mark_cnt[inv_ids[l]];
                int off_r = r == n ? mark_cnt.size() : mark_cnt[inv_ids[r]];
                REP(i, off_l, off_r) {
                    int x = mark_vs[i];
                    debug(x);
                    seg1.apply(idx[x], idx[x] + 1, { c, d });
                }
                seg2.apply(l - off_l, r - off_r, { c, d });
            });
        }
    }

    return 0;
}