#include <x86intrin.h>
#include <bits/stdc++.h>
using namespace std;

using str = string;
using ll = long long;
using ld = long double;
using u64 = unsigned long long;

template <class T>
using pr = pair<T, T>;
template <class T>
using vt = vector<T>;
template <class T>
using vvt = vector<vt<T>>;

#define ar array
#define pb push_back
#define fi first
#define se second
#define all(c) (c).begin(), (c).end()
#define len(x) (int)(x).size()
#define elif else if
#define def function

#define F_OR(i, a, b, s) for (int i=(a); (s)>0?i<(b):i>(b); i+=(s))
#define F_OR1(e) F_OR(i, 0, e, 1)
#define F_OR2(i, e) F_OR(i, 0, e, 1)
#define F_OR3(i, b, e) F_OR(i, b, e, 1)
#define F_OR4(i, b, e, s) F_OR(i, b, e, s)
#define GET5(a, b, c, d, e, ...) e
#define F_ORC(...) GET5(__VA_ARGS__, F_OR4, F_OR3, F_OR2, F_OR1)
#define rep(...) F_ORC(__VA_ARGS__)(__VA_ARGS__)
#define each(x, a) for (auto& x: a)

template <class T>
constexpr T inf = 0;
template <>
constexpr int inf<int> = 1'000'000'005;
template <>
constexpr long long inf<long long> = (long long)(inf<int>) * inf<int> * 2;
template <>
constexpr unsigned int inf<unsigned int> = inf<int>;
template <>
constexpr unsigned long long inf<unsigned long long> = inf<long long>;
template <>
constexpr __int128 inf<__int128> = __int128(inf<long long>) * inf<long long>;
template <>
constexpr double inf<double> = inf<long long>;
template <>
constexpr long double inf<long double> = inf<long long>;

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

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; }
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; }
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; }
template <typename T>
istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; }

void read() {}
template <typename T, class... U>
void read(T &t, U &...u) { cin >> t; read(u...); }
void print() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void print(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; print(u...); }
void write() { cout << " "; }
template <typename T, class... U, char sep = ' '>
void write(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; write(u...); }

#define Int(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define Ll(...)   \
  long long __VA_ARGS__; \
  read(__VA_ARGS__)
#define Str(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define Vt(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define Die(...)             \
  do {                       \
    print(__VA_ARGS__); \
    return 0;                  \
  } while (0)

__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
    return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
    return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
    if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long Pw(int n) { return 1LL << n; }
constexpr long long Msk(int n) { return (1LL << n) - 1; }

struct has_mod_impl {
    template <class T>
    static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
    template <class T>
    static auto check(...) -> std::false_type;
};

template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};

template <typename mint>
mint inv(int n) {
    static const int mod = mint::get_mod();
    static vector<mint> dat = {0, 1};
    assert(0 <= n);
    if (n >= mod) n %= mod;
    while (len(dat) <= n) {
        int k = len(dat);
        int q = (mod + k - 1) / k;
        dat.eb(dat[k * q - mod] * mint(q));
    }
    return dat[n];
}

template <typename mint>
mint fact(int n) {
    static const int mod = mint::get_mod();
    assert(0 <= n);
    if (n >= mod) return 0;
    static vector<mint> dat = {1, 1};
    while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint(len(dat)));
    return dat[n];
}

template <typename mint>
mint fact_inv(int n) {
    static vector<mint> dat = {1, 1};
    if (n < 0) return mint(0);
    while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
    return dat[n];
}

template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
    return (mint(1) * ... * fact_inv<mint>(xs));
}

template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
    return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}

template <typename mint>
mint C_dense(int n, int k) {
    static vector<vector<mint>> C;
    static int H = 0, W = 0;
    auto calc = [&](int i, int j) -> mint {
        if (i == 0) return (j == 0 ? mint(1) : mint(0));
        return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
    };
    if (W <= k) {
        for(int i = 0; i < H; i++) {
            C[i].resize(k + 1);
            for(int j = W; j < k + 1; j++) { C[i][j] = calc(i, j); }
        }
        W = k + 1;
    }
    if (H <= n) {
        C.resize(n + 1);
        for(int i = H; i < n + 1; i++) {
            C[i].resize(W);
            for(int j = 0; j < W; j++) { C[i][j] = calc(i, j); }
        }
        H = n + 1;
    }
    return C[n][k];
}

template <typename mint, bool large = false, bool dense = false>
mint C(long long n, long long k) {
    assert(n >= 0);
    if (k < 0 || n < k) return 0;
    if (dense) return C_dense<mint>(n, k);
    if (!large) return multinomial<mint>(n, k, n - k);
    k = min(k, n - k);
    mint x(1);
    for(int i = 0; i < k; i++) x *= mint(n - i);
    return x * fact_inv<mint>(k);
}

template <typename mint, bool large = false>
mint C_inv(long long n, long long k) {
    assert(n >= 0);
    assert(0 <= k && k <= n);
    if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
    return mint(1) / C<mint, 1>(n, k);
}

// [x^d] (1-x) ^ {-n} の計算
template <typename mint, bool large = false, bool dense = false>
mint C_negative(long long n, long long d) {
    assert(n >= 0);
    if (d < 0) return mint(0);
    if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
    return C<mint, large, dense>(n + d - 1, d);
}

template <int mod>
struct modint {
    static_assert(mod < (1 << 30));
    int val;
    constexpr modint(const long long val = 0) noexcept
            : val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {}
    bool operator<(const modint &other) const {
        return val < other.val;
    } // To use std::map
    modint &operator+=(const modint &p) {
        if ((val += p.val) >= mod) val -= mod;
        return *this;
    }
    modint &operator-=(const modint &p) {
        if ((val += mod - p.val) >= mod) val -= mod;
        return *this;
    }
    modint &operator*=(const modint &p) {
        val = (int)(1LL * val * p.val % mod);
        return *this;
    }
    modint &operator/=(const modint &p) {
        *this *= p.inverse();
        return *this;
    }
    modint operator-() const { return modint(-val); }
    modint operator+(const modint &p) const { return modint(*this) += p; }
    modint operator-(const modint &p) const { return modint(*this) -= p; }
    modint operator*(const modint &p) const { return modint(*this) *= p; }
    modint operator/(const modint &p) const { return modint(*this) /= p; }
    bool operator==(const modint &p) const { return val == p.val; }
    bool operator!=(const modint &p) const { return val != p.val; }
    modint inverse() const {
        int a = val, b = mod, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            swap(a -= t * b, b), swap(u -= t * v, v);
        }
        return modint(u);
    }
    modint pow(long long n) const {
        assert(n >= 0);
        modint ret(1), mul(val);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    void write() { write(val); }
    void read() {
        read(val);
        val = (val >= 0 ? val % mod : (mod - (-val) % mod) % mod);
    }

    static constexpr int get_mod() { return mod; }
    // (n, r), r は 1 の 2^n 乗根
    static constexpr pair<int, int> ntt_info() {
        if (mod == 167772161) return {25, 17};
        if (mod == 469762049) return {26, 30};
        if (mod == 754974721) return {24, 362};
        if (mod == 880803841) return {23, 211};
        if (mod == 998244353) return {23, 31};
        if (mod == 1045430273) return {20, 363};
        if (mod == 1051721729) return {20, 330};
        if (mod == 1053818881) return {20, 2789};
        return {-1, -1};
    }
    static constexpr bool can_ntt() { return ntt_info().first != -1; }
};

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;

// long でも大丈夫
// (val * x - 1) が mod の倍数になるようにする
// 特に mod=0 なら x=0 が満たす
long long mod_inv(long long val, long long mod) {
    if (mod == 0) return 0;
    mod = abs(mod);
    val %= mod;
    if (val < 0) val += mod;
    long long a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
        t = a / b;
        swap(a -= t * b, b), swap(u -= t * v, v);
    }
    if (u < 0) u += mod;
    return u;
}

template <class T>
vector<T> convolution_naive(const vector<T>& a, const vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    vector<T> ans(n + m - 1);
    if (n < m) {
        for(int j = 0; j < m; j++) for(int i = 0; i < n; i++) ans[i + j] += a[i] * b[j];
    } else {
        for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];
    }
    return ans;
}

template <class mint>
void ntt(vector<mint>& a, bool inverse) {
    assert(mint::can_ntt());
    const int rank2 = mint::ntt_info().first;
    const int mod = mint::get_mod();
    static array<mint, 30> root, iroot;
    static array<mint, 30> rate2, irate2;
    static array<mint, 30> rate3, irate3;

    static bool prepared = 0;
    if (!prepared) {
        prepared = 1;
        root[rank2] = mint::ntt_info().second;
        iroot[rank2] = mint(1) / root[rank2];
        for(int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }
        mint prod = 1, iprod = 1;
        for (int i = 0; i <= rank2 - 2; i++) {
            rate2[i] = root[i + 2] * prod;
            irate2[i] = iroot[i + 2] * iprod;
            prod *= iroot[i + 2];
            iprod *= root[i + 2];
        }
        prod = 1, iprod = 1;
        for (int i = 0; i <= rank2 - 3; i++) {
            rate3[i] = root[i + 3] * prod;
            irate3[i] = iroot[i + 3] * iprod;
            prod *= iroot[i + 3];
            iprod *= root[i + 3];
        }
    }

    int n = int(a.size());
    int h = (n == 0 ? -1 : 31 - __builtin_clz(n));
    assert(n == 1 << h);
    if (!inverse) {
        int len = 0;
        while (len < h) {
            if (h - len == 1) {
                int p = 1 << (h - len - 1);
                mint rot = 1;
                for(int s = 0; s < 1 << len; s++) {
                    int offset = s << (h - len);
                    for(int i = 0; i < p; i++) {
                        auto l = a[i + offset];
                        auto r = a[i + offset + p] * rot;
                        a[i + offset] = l + r;
                        a[i + offset + p] = l - r;
                    }
                    rot *= rate2[((~s & -~s) == 0 ? -1 : 31 - __builtin_clz(~s & -~s))];
                }
                len++;
            } else {
                int p = 1 << (h - len - 2);
                mint rot = 1, imag = root[2];
                for (int s = 0; s < (1 << len); s++) {
                    mint rot2 = rot * rot;
                    mint rot3 = rot2 * rot;
                    int offset = s << (h - len);
                    for (int i = 0; i < p; i++) {
                        unsigned long long mod2 = (unsigned long long)(mod) * mod;
                        unsigned long long a0 = a[i + offset].val;
                        unsigned long long a1 = (unsigned long long)(a[i + offset + p].val) * rot.val;
                        unsigned long long a2 = (unsigned long long)(a[i + offset + 2 * p].val) * rot2.val;
                        unsigned long long a3 = (unsigned long long)(a[i + offset + 3 * p].val) * rot3.val;
                        unsigned long long a1na3imag = (a1 + mod2 - a3) % mod * imag.val;
                        unsigned long long na2 = mod2 - a2;
                        a[i + offset] = a0 + a2 + a1 + a3;
                        a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                        a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                        a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                    }
                    rot *= rate3[((~s & -~s) == 0 ? -1 : 31 - __builtin_clz(~s & -~s))];
                }
                len += 2;
            }
        }
    } else {
        mint coef = mint(1) / mint((int) a.size());
        for(int i = 0; i < (int) a.size(); i++) a[i] *= coef;
        int len = h;
        while (len) {
            if (len == 1) {
                int p = 1 << (h - len);
                mint irot = 1;
                for(int s = 0; s < 1 << (len - 1); s++) {
                    int offset = s << (h - len + 1);
                    for(int i = 0; i < p; i++) {
                        unsigned long long l = a[i + offset].val;
                        unsigned long long r = a[i + offset + p].val;
                        a[i + offset] = l + r;
                        a[i + offset + p] = (mod + l - r) * irot.val;
                    }
                    irot *= irate2[((~s & -~s) == 0 ? -1 : 31 - __builtin_clz(~s & -~s))];
                }
                len--;
            } else {
                int p = 1 << (h - len);
                mint irot = 1, iimag = iroot[2];
                for(int s = 0; s < (1 << (len - 2)); s++) {
                    mint irot2 = irot * irot;
                    mint irot3 = irot2 * irot;
                    int offset = s << (h - len + 2);
                    for (int i = 0; i < p; i++) {
                        unsigned long long a0 = a[i + offset + 0 * p].val;
                        unsigned long long a1 = a[i + offset + 1 * p].val;
                        unsigned long long a2 = a[i + offset + 2 * p].val;
                        unsigned long long a3 = a[i + offset + 3 * p].val;
                        unsigned long long x = (mod + a2 - a3) * iimag.val % mod;
                        a[i + offset] = a0 + a1 + a2 + a3;
                        a[i + offset + 1 * p] = (a0 + mod - a1 + x) * irot.val;
                        a[i + offset + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * irot2.val;
                        a[i + offset + 3 * p] = (a0 + 2 * mod - a1 - x) * irot3.val;
                    }
                    irot *= irate3[((~s & -~s) == 0 ? -1 : 31 - __builtin_clz(~s & -~s))];
                }
                len -= 2;
            }
        }
    }
}

namespace CFFT {
    using real = double;

    struct C {
        real x, y;

        C() : x(0), y(0) {}

        C(real x, real y) : x(x), y(y) {}
        inline C operator+(const C& c) const { return C(x + c.x, y + c.y); }
        inline C operator-(const C& c) const { return C(x - c.x, y - c.y); }
        inline C operator*(const C& c) const {
            return C(x * c.x - y * c.y, x * c.y + y * c.x);
        }

        inline C conj() const { return C(x, -y); }
    };

    const real PI = acosl(-1);
    int base = 1;
    vector<C> rts = {{0, 0}, {1, 0}};
    vector<int> rev = {0, 1};

    void ensure_base(int nbase) {
        if (nbase <= base) return;
        rev.resize(1 << nbase);
        rts.resize(1 << nbase);
        for (int i = 0; i < (1 << nbase); i++) {
            rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
        }
        while (base < nbase) {
            real angle = PI * 2.0 / (1 << (base + 1));
            for (int i = 1 << (base - 1); i < (1 << base); i++) {
                rts[i << 1] = rts[i];
                real angle_i = angle * (2 * i + 1 - (1 << base));
                rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
            }
            ++base;
        }
    }

    void fft(vector<C>& a, int n) {
        assert((n & (n - 1)) == 0);
        int zeros = __builtin_ctz(n);
        ensure_base(zeros);
        int shift = base - zeros;
        for (int i = 0; i < n; i++) {
            if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); }
        }
        for (int k = 1; k < n; k <<= 1) {
            for (int i = 0; i < n; i += 2 * k) {
                for (int j = 0; j < k; j++) {
                    C z = a[i + j + k] * rts[j + k];
                    a[i + j + k] = a[i + j] - z;
                    a[i + j] = a[i + j] + z;
                }
            }
        }
    }
} // namespace CFFT

template <class mint>
vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {
    if (a.empty() || b.empty()) return {};
    int n = int(a.size()), m = int(b.size());
    int sz = 1;
    while (sz < n + m - 1) sz *= 2;

    // sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。
    if ((n + m - 3) <= sz / 2) {
        auto a_last = a.back(), b_last = b.back();
        a.pop_back(), b.pop_back();
        auto c = convolution(a, b);
        c.resize(n + m - 1);
        c[n + m - 2] = a_last * b_last;
        for(int i = 0; i < (int) a.size(); i++) c[i + (int) b.size()] += a[i] * b_last;
        for(int i = 0; i < (int) b.size(); i++) c[i + (int) a.size()] += b[i] * a_last;
        return c;
    }

    a.resize(sz), b.resize(sz);
    bool same = a == b;
    ntt(a, 0);
    if (same) {
        b = a;
    } else {
        ntt(b, 0);
    }
    for(int i = 0; i < sz; i++) a[i] *= b[i];
    ntt(a, 1);
    a.resize(n + m - 1);
    return a;
}

template <typename mint>
vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) {
    int n = (int) a.size(), m = (int) b.size();
    if (!n || !m) return {};
    static const long long nttprimes[] = {754974721, 167772161, 469762049};
    using mint0 = modint<754974721>;
    using mint1 = modint<167772161>;
    using mint2 = modint<469762049>;
    vector<mint0> a0(n), b0(m);
    vector<mint1> a1(n), b1(m);
    vector<mint2> a2(n), b2(m);
    for(int i = 0; i < n; i++) a0[i] = a[i].val, a1[i] = a[i].val, a2[i] = a[i].val;
    for(int i = 0; i < m; i++) b0[i] = b[i].val, b1[i] = b[i].val, b2[i] = b[i].val;
    auto c0 = convolution_ntt<mint0>(a0, b0);
    auto c1 = convolution_ntt<mint1>(a1, b1);
    auto c2 = convolution_ntt<mint2>(a2, b2);
    static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
    static const long long m0_inv_m1 = mint1(nttprimes[0]).inverse().val;
    static const long long m01_inv_m2 = mint2(m01).inverse().val;
    const int mod = mint::get_mod();
    auto garner = [&](mint0 x0, mint1 x1, mint2 x2) -> mint {
        int r0 = x0.val, r1 = x1.val, r2 = x2.val;
        int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
        auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * mint2(m01_inv_m2);
        return mint(r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val);
    };
    vector<mint> c((int) c0.size());
    for(int i = 0; i < (int) c.size(); i++) c[i] = garner(c0[i], c1[i], c2[i]);
    return c;
}

template <typename R>
vector<double> convolution_fft(const vector<R>& a, const vector<R>& b) {
    using C = CFFT::C;
    int need = (int)a.size() + (int)b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < need) nbase++;
    CFFT::ensure_base(nbase);
    int sz = 1 << nbase;
    vector<C> fa(sz);
    for (int i = 0; i < sz; i++) {
        int x = (i < (int)a.size() ? a[i] : 0);
        int y = (i < (int)b.size() ? b[i] : 0);
        fa[i] = C(x, y);
    }
    CFFT::fft(fa, sz);
    C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
    for (int i = 0; i <= (sz >> 1); i++) {
        int j = (sz - i) & (sz - 1);
        C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
        fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
        fa[i] = z;
    }
    for (int i = 0; i < (sz >> 1); i++) {
        C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
        C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * CFFT::rts[(sz >> 1) + i];
        fa[i] = A0 + A1 * s;
    }
    CFFT::fft(fa, sz >> 1);
    vector<double> ret(need);
    for (int i = 0; i < need; i++) {
        ret[i] = (i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
}

vector<long long> convolution(const vector<long long>& a, const vector<long long>& b) {
    int n = (int) a.size(), m = (int) b.size();
    if (!n || !m) return {};
    if (min(n, m) <= 60) return convolution_naive(a, b);
    long long abs_sum_a = 0, abs_sum_b = 0;
    long long LIM = 1e15;
    for(int i = 0; i < n; i++) abs_sum_a = min(LIM, abs_sum_a + abs(a[i]));
    for(int i = 0; i < m; i++) abs_sum_b = min(LIM, abs_sum_b + abs(b[i]));
    if (__int128(abs_sum_a) * abs_sum_b < 1e15) {
        vector<double> c = convolution_fft<long long>(a, b);
        vector<long long> res((int) c.size());
        for(int i = 0; i < (int) c.size(); i++) res[i] = (long long)(floor(c[i] + .5));
        return res;
    }

    static constexpr unsigned long long MOD1 = 754974721; // 2^24
    static constexpr unsigned long long MOD2 = 167772161; // 2^25
    static constexpr unsigned long long MOD3 = 469762049; // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

    static const unsigned long long i1 = mod_inv(MOD2 * MOD3, MOD1);
    static const unsigned long long i2 = mod_inv(MOD1 * MOD3, MOD2);
    static const unsigned long long i3 = mod_inv(MOD1 * MOD2, MOD3);

    using mint1 = modint<MOD1>;
    using mint2 = modint<MOD2>;
    using mint3 = modint<MOD3>;

    vector<mint1> a1(n), b1(m);
    vector<mint2> a2(n), b2(m);
    vector<mint3> a3(n), b3(m);
    for(int i = 0; i < n; i++) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];
    for(int i = 0; i < m; i++) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];

    auto c1 = convolution_ntt<mint1>(a1, b1);
    auto c2 = convolution_ntt<mint2>(a2, b2);
    auto c3 = convolution_ntt<mint3>(a3, b3);

    vector<long long> c(n + m - 1);
    for(int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i].val * i1) % MOD1 * M2M3;
        x += (c2[i].val * i2) % MOD2 * M1M3;
        x += (c3[i].val * i3) % MOD3 * M1M2;
        long long diff = c1[i].val - ((long long)(x) % (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5]
                = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }
    return c;
}

template <typename mint>
vector<mint> convolution(const vector<mint>& a, const vector<mint>& b) {
    int n = (int) a.size(), m = (int) b.size();
    if (!n || !m) return {};
    if (mint::can_ntt()) {
        if (min(n, m) <= 50) return convolution_naive(a, b);
        return convolution_ntt(a, b);
    }
    if (min(n, m) <= 200) return convolution_naive(a, b);
    return convolution_garner(a, b);
}

namespace dbg{
    // DEBUG BEGIN
    #ifndef ONLINE_JUDGE
    template<class L, class R> ostream &operator<<(ostream &out, const pair<L, R> &p){
    	return out << "{" << p.first << ", " << p.second << "}";
    }
    template<class Tuple, size_t N> struct _tuple_printer{
    	static ostream &_print(ostream &out, const Tuple &t){ return _tuple_printer<Tuple, N-1>::_print(out, t) << ", " << get<N-1>(t); }
    };
    template<class Tuple> struct _tuple_printer<Tuple, 1>{
    	static ostream &_print(ostream &out, const Tuple& t){ return out << get<0>(t); }
    };
    template<class... Args> ostream &_print_tuple(ostream &out, const tuple<Args...> &t){
    	return _tuple_printer<decltype(t), sizeof...(Args)>::_print(out << "{", t) << "}";
    }
    template<class ...Args> ostream &operator<<(ostream &out, const tuple<Args...> &t){
    	return _print_tuple(out, t);
    }
    template<class T> ostream &operator<<(class enable_if<!is_same<T, string>::value, ostream>::type &out, const T &arr){
    	if(arr.empty()) return out << "{}";
    	out << "{";
    	for(auto it = arr.begin(); it != arr.end(); ++ it){
    		out << *it;
    		next(it) != arr.end() ? out << ", " : out << "}";
    	}
    	return out;
    }
    ostream &operator<<(ostream &out, const _Bit_reference &bit){
    	return out << bool(bit);
    }
    template<class T, class A, class C>
    ostream &operator<<(ostream &out, priority_queue<T, A, C> pq){
    	vector<T> a;
    	while(!pq.empty()) a.push_back(pq.top()), pq.pop();
    	return out << a;
    }
    template<class Head>
    void debug_out(Head H){ cerr << H << endl; }
    template<class Head, class... Tail>
    void debug_out(Head H, Tail... T){ cerr << H << ", ", debug_out(T...); }
    void debug2_out(){ }
    template<class Head, class... Tail>
    void debug2_out(Head H, Tail... T){ cerr << "\n"; for(auto x: H) cerr << x << ",\n"; debug2_out(T...); }
    template<class Width, class Head>
    void debugbin_out(Width w, Head H){
    	for(auto rep = w; rep; -- rep, H >>= 1) cerr << (H & 1);
    	cerr << endl;
    }
    template<class Width, class Head, class... Tail>
    void debugbin_out(Width w, Head H, Tail... T){
    	for(auto rep = w; rep; -- rep, H >>= 1) cerr << (H & 1);
    	cerr << ", "; debugbin_out(w, T...);
    }
    enum CODE{ CCRED = 31, CCGREEN = 32, CCYELLOW = 33, CCBLUE = 34, CCDEFAULT = 39 };
    #define debug_endl() cerr << endl
    #define debug(...) cerr << "\033[" << (int)CODE(CCRED) << "m[" << #__VA_ARGS__ << "]: \033[" << (int)CODE(CCBLUE) << "m", debug_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
    #define debug2(...) cerr << "\033[" << (int)CODE(CCRED) << "m[" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debug2_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
    #define debugbin(...) cerr << "\033[" << (int)CODE(CCRED) << "m[" << #__VA_ARGS__ << "] \033[" << (int)CODE(CCBLUE) << "m", debugbin_out(__VA_ARGS__), cerr << "\33[" << (int)CODE(CCDEFAULT) << "m"
    #else
    #define debug_endl() 42
    #define debug(...) 42
    #define debug2(...) 42
    #define debugbin(...) 42
    #endif
    // DEBUG END
} using namespace dbg;

signed main(){
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(ios::badbit | ios::failbit);
    auto __solve_tc = [&](auto __tc_num)->int {
        Ll(n, m);
        Vt(ll, a, n);
        int mx = -1;
        each(x, a) ctmax(mx, x);
        int lim = mx + 1;
        vt<ll> poly(lim);
        each(x, a) poly[x] += 1;
        auto ret = convolution(poly, poly);
        if (m >= len(ret)) Die(0);
        print(ret[m]);
        return 0;
    };
    int __tc_cnt = 1;
    for(auto __tc_num = 0; __tc_num < __tc_cnt; ++ __tc_num){
        __solve_tc(__tc_num);
    }
}