// #pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using vecint = std::vector<int>;
using vecll = std::vector<long long>;
using vecstr = std::vector<string>;
using vecbool = std::vector<bool>;
using vecdou = std::vector<double>;
using vecpl = std::vector<pair<ll,ll>>;
using vec2d = std::vector<vecll>;
using vec2di = std::vector<vecint>;
using vec2dd = std::vector<vecdou>;
using vec2db = std::vector<vecbool>;
using pl = pair<long long,long long>;
#define rep(i,n) for (ll i = 0; i < (ll)(n); i++)
#define rep1(i,n) for (ll i = 1; i <= (ll)(n); i++)
#define REP(i,l,r) for (ll i = (ll)(l); i < (ll)(r); i++)
#define rrep(i,n) for (ll i = (ll)(n)-1; i >= 0; i--)
#define rrep1(i,n) for (ll i = (ll)(n); i > 0; i--)
#define RREP(i,l,r) for (ll i = (ll)(r)-1; i >= (ll)(l); i--)
#define all(a) (a).begin(), (a).end()
#define INF ((1LL<<62)-(1LL<<31))
#define inr(a,x,b) ((a) <= (x) && (x) < (b))
template <typename T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <typename T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

void ynout(bool x,string Tru="Yes",string Wro="No"){
    if(x){
        cout << Tru << '\n';
    }else{
        cout << Wro << '\n';
    }
}
ll power(ll a,ll b,ll mod=INF){
    long long x=1,y=a%mod;
    while(b>0){
        if(b&1ll){
            x=(x*y)%mod;
        }
        y=(y*y)%mod;
        b>>=1;
    }
  return x%mod;
}
ll Pdist2(pair<ll,ll> a,pair<ll,ll> b){
    return (a.first-b.first)*(a.first-b.first)+(a.second-b.second)*(a.second-b.second);
}
double Pdist(pair<ll,ll> a,pair<ll,ll> b){
    return sqrt(Pdist2(a,b));
}
ll PdistM(pair<ll,ll> a,pair<ll,ll> b){
    return abs(a.first-b.first)+abs(a.second-b.second);
}
ll gcd(ll a,ll b){
    if(b==0){
        return a;
    }else{
        return gcd(b,a%b);
    }
}
ll lcm(ll a,ll b){
    return a/gcd(a,b)*b;
}
template <typename T>
void print(const std::vector<T>& v) {
    for (const auto& elem : v) {
        cout << elem << " ";
    }
    cout << '\n';
}
template <typename T>
void print2d(const std::vector<std::vector<T>>& v) {
    for (const auto& row : v) {
        for (const auto& elem : row) {
            cout << elem << " ";
        }
        cout << '\n';
    }
}
vecll vecinp(ll n){
    vecll v(n);
    rep(i,n) cin >> v[i];
    return v;
}


void solve();

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
    ll t=1;
    // std::cin >> t;
    rep(i,t)solve();
}

// vecll dx = {1,0,-1,0};
// vecll dy = {0,1,0,-1};
// vector<char> dir = {'D','R','U','L'};

// begin include: atcoder/modint
// begin include: atcoder/modint.hpp

#include <cassert>
#include <numeric>
#include <type_traits>

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

// begin include: atcoder/internal_math
// begin include: atcoder/internal_math.hpp

#include <utility>

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

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder

// end include: atcoder/internal_math.hpp
// end include: atcoder/internal_math
// begin include: atcoder/internal_type_traits
// begin include: atcoder/internal_type_traits.hpp

#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder

// end include: atcoder/internal_type_traits.hpp
// end include: atcoder/internal_type_traits

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

// end include: atcoder/modint.hpp
// end include: atcoder/modint
// begin include: libraries/HLD_seg_edge.hpp
#include <bits/stdc++.h>
// begin include: atcoder/segtree
// begin include: atcoder/segtree.hpp

#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>

// begin include: atcoder/internal_bit
// begin include: atcoder/internal_bit.hpp

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

#if __cplusplus >= 202002L
#include <bit>
#endif

namespace atcoder {

namespace internal {

#if __cplusplus >= 202002L

using std::bit_ceil;

#else

// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
    unsigned int x = 1;
    while (x < (unsigned int)(n)) x *= 2;
    return x;
}

#endif

// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

}  // namespace internal

}  // namespace atcoder

// end include: atcoder/internal_bit.hpp
// end include: atcoder/internal_bit

namespace atcoder {

#if __cplusplus >= 201703L

template <class S, auto op, auto e> struct segtree {
    static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                  "op must work as S(S, S)");
    static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                  "e must work as S()");

#else

template <class S, S (*op)(S, S), S (*e)()> struct segtree {

#endif

  public:
    segtree() : segtree(0) {}
    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        size = (int)internal::bit_ceil((unsigned int)(_n));
        log = internal::countr_zero((unsigned int)size);
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder

// end include: atcoder/segtree.hpp
// end include: atcoder/segtree
// begin include: edge.hpp

template <class S> struct edge {
    int from, to;
    S weight;
    edge(int from_, int to_, S weight_) : from(from_), to(to_), weight(weight_) {}
    edge() : from(-1), to(-1), weight() {}
};
// end include: edge.hpp
using namespace std;
using ll = long long;
using vecll = std::vector<long long>;
#define rep(i,n) for (ll i = 0; i < (ll)(n); i++)

template <class S, auto op, auto e> struct HLD_seg_edge {
    vecll vertex;
    vecll id;
    vecll head;
    vecll parent;
    vecll depth;
    vecll subsize;
    vecll heavy_child;
    int root;

    static S op_rev(S a, S b) {
        return op(b, a);
    }
    atcoder::segtree<S, op, e> seg;
    atcoder::segtree<S, op_rev, e> seg_rev;

    vecll edge_id;

    HLD_seg_edge(int n, const vector<edge<S>>& edges, int root_ = 0) {
        root = root_;
        vertex.resize(n);
        id.resize(n);
        head.resize(n);
        parent.resize(n);
        depth.resize(n);
        subsize.resize(n);
        heavy_child.resize(n);
        seg = atcoder::segtree<S, op, e>(n);
        seg_rev = atcoder::segtree<S, op_rev, e>(n);
        edge_id.resize(n-1);
        vector<vector<ll>> graph(n);
        for (const auto& edge : edges) {
            int u = edge.from, v = edge.to;
            graph[u].emplace_back(v);
            graph[v].emplace_back(u);
        }
        {
            function<void(int,int,int)> dfs = [&](int v, int p, int d) {
                parent[v] = p;
                depth[v] = d;
                subsize[v] = 1;
                heavy_child[v] = -1;
                int max_subsize = 0;
                for (int to : graph[v]) {
                    if (to == p) continue;
                    dfs(to, v, d + 1);
                    subsize[v] += subsize[to];
                    if (subsize[to] > max_subsize) {
                        max_subsize = subsize[to];
                        heavy_child[v] = to;
                    }
                }
            };
            dfs(root, -1, 0);
        }
        {
            int idx = 0;
            function<void(int,int)> dfs = [&](int v, int h) {
                head[v] = h;
                id[v] = idx;
                vertex[idx] = v;
                idx++;
                if (heavy_child[v] != -1) {
                    dfs(heavy_child[v], h);
                }
                for (int to : graph[v]) {
                    if (to == parent[v] || to == heavy_child[v]) continue;
                    dfs(to, to);
                }
            };
            dfs(root, root);
        }
        rep(i,edges.size()) {
            const auto& edge = edges[i];
            int u = edge.from, v = edge.to;
            S w = edge.weight;
            if (parent[v] == u) {
                seg.set(id[v], w);
                seg_rev.set(id[v], w);
                edge_id[i] = id[v];
            } else {
                seg.set(id[u], w);
                seg_rev.set(id[u], w);
                edge_id[i] = id[u];
            }
        }
    }

    // vの祖先で深さがdのものを返す
    int level_ancestor(int v, int d) {
        if (depth[v] < d) return -1;
        while (depth[head[v]] > d) {
            v = parent[head[v]];
        }
        return vertex[id[v] - (depth[v] - d)];
    }

    // uとvのLCAを返す
    int lca(int u, int v) {
        while (head[u] != head[v]) {
            if (depth[head[u]] > depth[head[v]]) {
                u = parent[head[u]];
            } else {
                v = parent[head[v]];
            }
        }
        return depth[u] < depth[v] ? u : v;
    }

    // uとvの距離を返す
    int distance(int u, int v) {
        int l = lca(u, v);
        return depth[u] + depth[v] - 2 * depth[l];
    }

    // s->tのパス上i番目の頂点を返す
    int jump(int s, int t, int i) {
        int l = lca(s, t);
        if (i <= depth[s] - depth[l]) {
            return level_ancestor(s, depth[s] - i);
        } else {
            return level_ancestor(t, i - depth[s]  + 2*depth[l]);
        }
    }

    // 辺vの値をxに更新
    void set(int v, S x) {
        seg.set(edge_id[v], x);
        seg_rev.set(edge_id[v], x);
    }

    S get(int i) {
        return seg.get(edge_id[i]);
    }

    // s->tのパス(e0,...,ek)に対し、e0・...・ekを返す
    S prod_path(int s, int t) {
        int l = lca(s, t);
        S res_left = e(), res_right = e();
        while (head[s] != head[l]) {
            res_left = op(res_left, seg_rev.prod(id[head[s]], id[s] + 1));
            s = parent[head[s]];
        }
        res_left = op(res_left, seg_rev.prod(id[l] + 1, id[s] + 1));
        while (head[t] != head[l]) {
            res_right = op(seg.prod(id[head[t]], id[t] + 1), res_right);
            t = parent[head[t]];
        }
        res_right = op(seg.prod(id[l] + 1, id[t] + 1), res_right);
        return op(res_left, res_right);
    }
};
// end include: libraries/HLD_seg_edge.hpp

using S = vector<vector<atcoder::modint1000000007>>;


S op(S a, S b) {
    int n = 2;
    S res(n, vector<atcoder::modint1000000007>(n, 0));
    rep(i,n)rep(j,n)rep(k,n){
        res[i][j] += a[i][k] * b[k][j];
    }
    return res;
}
S e() {
    int n = 2;
    S res(n, vector<atcoder::modint1000000007>(n, 0));
    rep(i,n) res[i][i] = 1;
    return res;
}

void solve(){
    ll n;
    cin>>n;
    vector<edge<S>> E(n-1);
    rep(i,n-1){
        ll u,v;
        cin>>u>>v;
        E[i] = edge<S>(u, v, e());
    }
    HLD_seg_edge<S,op,e> hld(n, E);
    ll q;
    cin>>q;
    while(q--){
        char t;
        cin>>t;
        if(t=='x'){
            ll i;
            S x(2, vector<atcoder::modint1000000007>(2));
            cin>>i;
            rep(a,2)rep(b,2){
                int val;
                cin>>val;
                x[a][b] = val;
            }
            hld.set(i,x);
        }else {
            ll u,v;
            cin>>u>>v;
            auto res = hld.prod_path(u,v);
            rep(i,2){
                rep(j,2) cout << res[i][j].val() << " ";
            }
            cout << '\n';
        }
    }
}