// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;

namespace templates {
// type
using ll  = long long;
using ull = unsigned long long;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));

// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)

// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on

// const value
const ll MOD1   = 1000000007;
const ll MOD9   = 998244353;
const double PI = acos(-1);

// other macro
#ifndef RIN__LOCAL
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)

// function
vector<char> stoc(string &S) {
    int n = S.size();
    vector<char> ret(n);
    for (int i = 0; i < n; i++) ret[i] = S[i];
    return ret;
}
string ctos(vector<char> &S) {
    int n      = S.size();
    string ret = "";
    for (int i = 0; i < n; i++) ret += S[i];
    return ret;
}

template <class T>
auto min(const T &a) {
    return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
    return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
    return (a > r ? r : a < l ? l : a);
}
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);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
    auto b = clamp(a, l, r);
    return (a != b ? a = b, 1 : 0);
}

template <typename T>
T sum(vector<T> &A) {
    T tot = 0;
    for (auto a : A) tot += a;
    return tot;
}

template <typename T>
vector<T> compression(vector<T> X) {
    sort(all(X));
    X.erase(unique(all(X)), X.end());
    return X;
}

// input and output
namespace io {

// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << ' ';
    }
    return os;
}

// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
    for (auto &a : A) is >> a;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}

// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
    is >> A.first >> A.second;
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
    os << A.first << ' ' << A.second;
    return os;
}

// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        is >> A[i];
    }
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
    for (size_t i = 0; i < A.size(); i++) {
        os << A[i];
        if (i != A.size() - 1) os << endl;
    }
    return os;
}

// set<T>
template <typename T>
ostream &operator<<(ostream &os, set<T> &A) {
    for (auto itr = A.begin(); itr != A.end(); itr++) {
        os << *itr;
        if (next(itr) != A.end()) os << ' ';
    }
    return os;
}

// unordered_set<T>
template <typename T>
ostream &operator<<(ostream &os, unordered_set<T> &A) {
    for (auto itr = A.begin(); itr != A.end(); itr++) {
        os << *itr;
        if (next(itr) != A.end()) os << ' ';
    }
    return os;
}

// multiset<T>
template <typename T>
ostream &operator<<(ostream &os, multiset<T> &A) {
    for (auto itr = A.begin(); itr != A.end(); itr++) {
        os << *itr;
        if (next(itr) != A.end()) os << ' ';
    }
    return os;
}

// unordered_multiset<T>
template <typename T>
ostream &operator<<(ostream &os, unordered_multiset<T> &A) {
    for (auto itr = A.begin(); itr != A.end(); itr++) {
        os << *itr;
        if (next(itr) != A.end()) os << endl;
    }
    return os;
}

// map<S, T>
template <typename S, typename T>
ostream &operator<<(ostream &os, map<S, T> &A) {
    for (auto itr = A.begin(); itr != A.end(); itr++) {
        os << *itr;
        if (next(itr) != A.end()) os << endl;
    }
    return os;
}

// unordered_map<S, T>
template <typename S, typename T>
ostream &operator<<(ostream &os, unordered_map<S, T> &A) {
    for (auto itr = A.begin(); itr != A.end(); itr++) {
        os << *itr;
        if (next(itr) != A.end()) os << endl;
    }
    return os;
}

// tuple
template <typename T, size_t N>
struct TuplePrint {
    static ostream &print(ostream &os, const T &t) {
        TuplePrint<T, N - 1>::print(os, t);
        os << ' ' << get<N - 1>(t);
        return os;
    }
};
template <typename T>
struct TuplePrint<T, 1> {
    static ostream &print(ostream &os, const T &t) {
        os << get<0>(t);
        return os;
    }
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
    TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
    return os;
}

// queue<T>
template <typename T>
ostream &operator<<(ostream &os, queue<T> &A) {
    auto B = A;
    while (!B.empty()) {
        os << B.front();
        B.pop();
        if (!B.empty()) os << ' ';
    }
    return os;
}

// deque<T>
template <typename T>
ostream &operator<<(ostream &os, deque<T> &A) {
    auto B = A;
    while (!B.empty()) {
        os << B.front();
        B.pop_front();
        if (!B.empty()) os << ' ';
    }
    return os;
}

// stack<T>
template <typename T>
ostream &operator<<(ostream &os, stack<T> &A) {
    auto B = A;
    stack<T> C;
    while (!B.empty()) {
        C.push(B.top());
        B.pop();
    }
    while (!C.empty()) {
        os << C.top();
        C.pop();
        if (!C.empty()) os << ' ';
    }
    return os;
}

// priority_queue<T>
template <typename T>
ostream &operator<<(ostream &os, priority_queue<T> &A) {
    auto B = A;
    while (!B.empty()) {
        os << B.top();
        B.pop();
        if (!B.empty()) os << endl;
    }
    return os;
}

// bitset<N>
template <size_t N>
ostream &operator<<(ostream &os, bitset<N> &A) {
    for (size_t i = 0; i < N; i++) {
        os << A[i];
    }
    return os;
}

// io functions
void FLUSH() {
    cout << flush;
}

void print() {
    cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail)) cout << spa;
    print(forward<Tail>(tail)...);
}

template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
    int n = A.size();
    for (int i = 0; i < n; i++) {
        cout << A[i];
        if (i != n - 1) cout << sep;
    }
    cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
    cout << A << end;
}
template <typename T>
void prispa(T A) {
    priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
    if (f)
        print(A);
    else
        print(B);
    return f;
}

template <class... T>
void inp(T &...a) {
    (cin >> ... >> a);
}

} // namespace io
using namespace io;

// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<int>> edges(n, vector<int>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        u -= indexed;
        v -= indexed;
        edges[u].push_back(v);
        if (!direct) edges[v].push_back(u);
    }
    return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
    return read_edges(n, n - 1, false, indexed);
}

template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
    vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
    for (int i = 0; i < m; i++) {
        INT(u, v);
        T w;
        inp(w);
        u -= indexed;
        v -= indexed;
        edges[u].push_back({v, w});
        if (!direct) edges[v].push_back({u, w});
    }
    return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
    return read_wedges<T>(n, n - 1, false, indexed);
}

// yes / no
namespace yesno {

// yes
inline bool yes(bool f = true) {
    cout << (f ? "yes" : "no") << endl;
    return f;
}
inline bool Yes(bool f = true) {
    cout << (f ? "Yes" : "No") << endl;
    return f;
}
inline bool YES(bool f = true) {
    cout << (f ? "YES" : "NO") << endl;
    return f;
}

// no
inline bool no(bool f = true) {
    cout << (!f ? "yes" : "no") << endl;
    return f;
}
inline bool No(bool f = true) {
    cout << (!f ? "Yes" : "No") << endl;
    return f;
}
inline bool NO(bool f = true) {
    cout << (!f ? "YES" : "NO") << endl;
    return f;
}

// possible
inline bool possible(bool f = true) {
    cout << (f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Possible(bool f = true) {
    cout << (f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool POSSIBLE(bool f = true) {
    cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}

// impossible
inline bool impossible(bool f = true) {
    cout << (!f ? "possible" : "impossible") << endl;
    return f;
}
inline bool Impossible(bool f = true) {
    cout << (!f ? "Possible" : "Impossible") << endl;
    return f;
}
inline bool IMPOSSIBLE(bool f = true) {
    cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
    return f;
}

// Alice Bob
inline bool Alice(bool f = true) {
    cout << (f ? "Alice" : "Bob") << endl;
    return f;
}
inline bool Bob(bool f = true) {
    cout << (f ? "Bob" : "Alice") << endl;
    return f;
}

// Takahashi Aoki
inline bool Takahashi(bool f = true) {
    cout << (f ? "Takahashi" : "Aoki") << endl;
    return f;
}
inline bool Aoki(bool f = true) {
    cout << (f ? "Aoki" : "Takahashi") << endl;
    return f;
}

} // namespace yesno
using namespace yesno;

} // namespace templates
using namespace templates;

template <typename mint>
struct NumberTheoreticTransform {
    static vector<mint> roots, iroots, rate3, irate3;
    static int max_base;

    NumberTheoreticTransform() = default;

    static void init() {
        if (!roots.empty()) return;
        const unsigned mod = mint::get_mod();
        auto tmp           = mod - 1;
        max_base           = 0;
        while (tmp % 2 == 0) {
            tmp >>= 1;
            max_base++;
        }
        mint root = 2;
        while (root.pow((mod - 1) >> 1) == 1) root++;

        roots.resize(max_base + 1);
        iroots.resize(max_base + 1);
        rate3.resize(max_base + 1);
        irate3.resize(max_base + 1);

        roots[max_base]  = root.pow((mod - 1) >> max_base);
        iroots[max_base] = mint(1) / roots[max_base];
        for (int i = max_base - 1; i >= 0; i--) {
            roots[i]  = roots[i + 1] * roots[i + 1];
            iroots[i] = iroots[i + 1] * iroots[i + 1];
        }

        mint prod = 1, iprod = 1;
        for (int i = 0; i <= max_base - 3; i++) {
            rate3[i]  = roots[i + 3] * prod;
            irate3[i] = iroots[i + 3] * iprod;
            prod *= iroots[i + 3];
            iprod *= roots[i + 3];
        }
    }

    static void ntt(vector<mint> &A) {
        init();
        int n     = A.size();
        int h     = __builtin_ctz(n);
        int le    = 0;
        mint imag = roots[2];
        if (h & 1) {
            int p = 1 << (h - 1);
            for (int i = 0; i < p; i++) {
                auto r   = A[i + p];
                A[i + p] = A[i] - r;
                A[i] += r;
            }
            le++;
        }
        for (; le + 1 < h; le += 2) {
            int p = 1 << (h - le - 2);

            for (int i = 0; i < p; i++) {
                auto a0        = A[i];
                auto a1        = A[i + p];
                auto a2        = A[i + 2 * p];
                auto a3        = A[i + 3 * p];
                auto a1na3imag = (a1 - a3) * imag;
                A[i]           = a0 + a2 + a1 + a3;
                A[i + p]       = a0 + a2 - (a1 + a3);
                A[i + 2 * p]   = a0 - a2 + a1na3imag;
                A[i + 3 * p]   = a0 - a2 - a1na3imag;
            }

            mint rot = rate3[0];
            for (int s = 1; s < (1 << le); s++) {
                int offset = s << (h - le);
                mint rot2  = rot * rot;
                mint rot3  = rot2 * rot;
                for (int i = 0; i < p; i++) {
                    auto a0               = A[i + offset];
                    auto a1               = A[i + offset + p] * rot;
                    auto a2               = A[i + offset + 2 * p] * rot2;
                    auto a3               = A[i + offset + 3 * p] * rot3;
                    auto a1na3imag        = (a1 - a3) * imag;
                    A[i + offset]         = a0 + a2 + a1 + a3;
                    A[i + offset + p]     = a0 + a2 - (a1 + a3);
                    A[i + offset + 2 * p] = a0 - a2 + a1na3imag;
                    A[i + offset + 3 * p] = a0 - a2 - a1na3imag;
                }
                rot *= rate3[__builtin_ctz(~s)];
            }
        }
    }

    static void intt(vector<mint> &A, bool f = true) {
        init();
        int n      = A.size();
        int h      = __builtin_ctz(n);
        int le     = h;
        mint iimag = iroots[2];
        for (; le > 1; le -= 2) {
            int p = 1 << (h - le);

            for (int i = 0; i < p; i++) {
                auto a0         = A[i];
                auto a1         = A[i + p];
                auto a2         = A[i + 2 * p];
                auto a3         = A[i + 3 * p];
                auto a2na3iimag = (a2 - a3) * iimag;
                A[i]            = a0 + a1 + a2 + a3;
                A[i + p]        = a0 - a1 + a2na3iimag;
                A[i + 2 * p]    = a0 + a1 - (a2 + a3);
                A[i + 3 * p]    = a0 - a1 - a2na3iimag;
            }

            mint irot = irate3[0];
            for (int s = 1; s < (1 << (le - 2)); s++) {
                int offset = s << (h - le + 2);
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                for (int i = 0; i < p; i++) {
                    auto a0               = A[i + offset];
                    auto a1               = A[i + offset + p];
                    auto a2               = A[i + offset + 2 * p];
                    auto a3               = A[i + offset + 3 * p];
                    auto a2na3iimag       = (a2 - a3) * iimag;
                    A[i + offset]         = a0 + a1 + a2 + a3;
                    A[i + offset + p]     = (a0 - a1 + a2na3iimag) * irot;
                    A[i + offset + 2 * p] = (a0 + a1 - (a2 + a3)) * irot2;
                    A[i + offset + 3 * p] = (a0 - a1 - a2na3iimag) * irot3;
                }
                irot *= irate3[__builtin_ctz(~s)];
            }
        }
        if (le >= 1) {
            int p = 1 << (h - 1);
            for (int i = 0; i < p; i++) {
                auto ajp = A[i] - A[i + p];
                A[i] += A[i + p];
                A[i + p] = ajp;
            }
        }
        if (f) {
            mint inv = mint(1) / n;
            for (int i = 0; i < n; i++) {
                A[i] *= inv;
            }
        }
    }

    static vector<mint> multiply(vector<mint> A, vector<mint> B) {
        int need = A.size() + B.size() - 1;
        if (min(A.size(), B.size()) < 60) {
            vector<mint> C(need, 0);
            for (size_t i = 0; i < A.size(); i++)
                for (size_t j = 0; j < B.size(); j++) {
                    C[i + j] += A[i] * B[j];
                }
            return C;
        }
        int sz = 1;
        while (sz < need) sz <<= 1;
        A.resize(sz, 0);
        B.resize(sz, 0);
        ntt(A);
        ntt(B);
        mint inv = mint(1) / sz;
        for (int i = 0; i < sz; i++) A[i] *= B[i] * inv;
        intt(A, false);
        A.resize(need);
        return A;
    }
};

template <typename mint>
vector<mint> NumberTheoreticTransform<mint>::roots = vector<mint>();
template <typename mint>
vector<mint> NumberTheoreticTransform<mint>::iroots = vector<mint>();
template <typename mint>
vector<mint> NumberTheoreticTransform<mint>::rate3 = vector<mint>();
template <typename mint>
vector<mint> NumberTheoreticTransform<mint>::irate3 = vector<mint>();
template <typename mint>
int NumberTheoreticTransform<mint>::max_base = 0;

template <int MOD>
struct Modint {
    int x;
    Modint() : x(0) {}
    Modint(int64_t y) {
        if (y >= 0)
            x = y % MOD;
        else
            x = (y % MOD + MOD) % MOD;
    }

    Modint &operator+=(const Modint &p) {
        x += p.x;
        if (x >= MOD) x -= MOD;
        return *this;
    }

    Modint &operator-=(const Modint &p) {
        x -= p.x;
        if (x < 0) x += MOD;
        return *this;
    }

    Modint &operator*=(const Modint &p) {
        x = int(1LL * x * p.x % MOD);
        return *this;
    }

    Modint &operator/=(const Modint &p) {
        *this *= p.inverse();
        return *this;
    }

    Modint &operator%=(const Modint &p) {
        assert(p.x == 0);
        return *this;
    }

    Modint operator-() const {
        return Modint(-x);
    }

    Modint &operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }

    Modint &operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }

    Modint operator++(int) {
        Modint result = *this;
        ++*this;
        return result;
    }

    Modint operator--(int) {
        Modint result = *this;
        --*this;
        return result;
    }

    friend Modint operator+(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) += rhs;
    }

    friend Modint operator-(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) -= rhs;
    }

    friend Modint operator*(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) *= rhs;
    }

    friend Modint operator/(const Modint &lhs, const Modint &rhs) {
        return Modint(lhs) /= rhs;
    }

    friend Modint operator%(const Modint &lhs, const Modint &rhs) {
        assert(rhs.x == 0);
        return Modint(lhs);
    }

    bool operator==(const Modint &p) const {
        return x == p.x;
    }

    bool operator!=(const Modint &p) const {
        return x != p.x;
    }

    bool operator<(const Modint &rhs) const {
        return x < rhs.x;
    }

    bool operator<=(const Modint &rhs) const {
        return x <= rhs.x;
    }

    bool operator>(const Modint &rhs) const {
        return x > rhs.x;
    }

    bool operator>=(const Modint &rhs) const {
        return x >= rhs.x;
    }

    Modint inverse() const {
        int a = x, b = MOD, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            a -= t * b;
            u -= t * v;
            swap(a, b);
            swap(u, v);
        }
        return Modint(u);
    }

    Modint pow(int64_t k) const {
        Modint ret(1);
        Modint y(x);
        while (k > 0) {
            if (k & 1) ret *= y;
            y *= y;
            k >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Modint &p) {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, Modint &p) {
        int64_t y;
        is >> y;
        p = Modint<MOD>(y);
        return (is);
    }

    static int get_mod() {
        return MOD;
    }
};

struct Arbitrary_Modint {
    int x;
    static int MOD;

    static void set_mod(int mod) {
        MOD = mod;
    }

    Arbitrary_Modint() : x(0) {}
    Arbitrary_Modint(int64_t y) {
        if (y >= 0)
            x = y % MOD;
        else
            x = (y % MOD + MOD) % MOD;
    }

    Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) {
        x += p.x;
        if (x >= MOD) x -= MOD;
        return *this;
    }

    Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) {
        x -= p.x;
        if (x < 0) x += MOD;
        return *this;
    }

    Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) {
        x = int(1LL * x * p.x % MOD);
        return *this;
    }

    Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) {
        *this *= p.inverse();
        return *this;
    }

    Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) {
        assert(p.x == 0);
        return *this;
    }

    Arbitrary_Modint operator-() const {
        return Arbitrary_Modint(-x);
    }

    Arbitrary_Modint &operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }

    Arbitrary_Modint &operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }

    Arbitrary_Modint operator++(int) {
        Arbitrary_Modint result = *this;
        ++*this;
        return result;
    }

    Arbitrary_Modint operator--(int) {
        Arbitrary_Modint result = *this;
        --*this;
        return result;
    }

    friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) += rhs;
    }

    friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) -= rhs;
    }

    friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) *= rhs;
    }

    friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        return Arbitrary_Modint(lhs) /= rhs;
    }

    friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
        assert(rhs.x == 0);
        return Arbitrary_Modint(lhs);
    }

    bool operator==(const Arbitrary_Modint &p) const {
        return x == p.x;
    }

    bool operator!=(const Arbitrary_Modint &p) const {
        return x != p.x;
    }

    bool operator<(const Arbitrary_Modint &rhs) {
        return x < rhs.x;
    }

    bool operator<=(const Arbitrary_Modint &rhs) {
        return x <= rhs.x;
    }

    bool operator>(const Arbitrary_Modint &rhs) {
        return x > rhs.x;
    }

    bool operator>=(const Arbitrary_Modint &rhs) {
        return x >= rhs.x;
    }

    Arbitrary_Modint inverse() const {
        int a = x, b = MOD, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            a -= t * b;
            u -= t * v;
            swap(a, b);
            swap(u, v);
        }
        return Arbitrary_Modint(u);
    }

    Arbitrary_Modint pow(int64_t k) const {
        Arbitrary_Modint ret(1);
        Arbitrary_Modint y(x);
        while (k > 0) {
            if (k & 1) ret *= y;
            y *= y;
            k >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Arbitrary_Modint &p) {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, Arbitrary_Modint &p) {
        int64_t y;
        is >> y;
        p = Arbitrary_Modint(y);
        return (is);
    }

    static int get_mod() {
        return MOD;
    }
};
int Arbitrary_Modint::MOD = 998244353;

using modint9 = Modint<998244353>;
using modint1 = Modint<1000000007>;
using modint  = Arbitrary_Modint;
using mint    = modint9;
using NTT     = NumberTheoreticTransform<mint>;

void solve() {
    LL(x, y, t, a, b, c, d);
    ll h = 1 << (x + 1);
    ll w = 1 << (y + 1);
    vvec(mint, A, h, w, 0);
    a--;
    b--;
    c--;
    d--;
    A[a][b]++;
    A[a][w - 2 - b]--;
    A[h - 2 - a][b]--;
    A[h - 2 - a][w - 2 - b]++;

    vvec(mint, B, h, w, 0);
    B[0][0]     = 1;
    B[0][1]     = 1;
    B[0][w - 1] = 1;
    B[1][0]     = 1;
    B[h - 1][0] = 1;

    for (int i = 0; i < h; i++) {
        NTT::ntt(A[i]);
        NTT::ntt(B[i]);
    }
    for (int j = 0; j < w; j++) {
        vec(mint, C, h, 0);
        for (int i = 0; i < h; i++) {
            C[i] = A[i][j];
        }
        NTT::ntt(C);
        for (int i = 0; i < h; i++) {
            A[i][j] = C[i];
        }

        vec(mint, D, h, 0);
        for (int i = 0; i < h; i++) {
            D[i] = B[i][j];
        }
        NTT::ntt(D);
        for (int i = 0; i < h; i++) {
            B[i][j] = D[i];
        }
    }

    for (int i = 0; i < h; i++) {
        for (int j = 0; j < w; j++) {
            A[i][j] *= B[i][j].pow(t);
        }
    }

    for (int j = 0; j < w; j++) {
        vec(mint, C, h, 0);
        for (int i = 0; i < h; i++) {
            C[i] = A[i][j];
        }
        NTT::intt(C);
        for (int i = 0; i < h; i++) {
            A[i][j] = C[i];
        }
    }

    for (int i = 0; i < h; i++) {
        NTT::intt(A[i]);
    }

    mint ans = A[c][d];
    print(ans);
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    // cout << fixed << setprecision(12);
    int t;
    t = 1;
    // cin >> t;
    while (t--) solve();
    return 0;
}