#define PROBLEM "https://yukicoder.me/problems/no/214"
// #include "linear_algebra_matrix/linear_recurrence.hpp"
#pragma once
#include <algorithm>
#include <cassert>
#include <utility>
#include <vector>

// CUT begin
// Berlekamp–Massey algorithm
// <https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm>
// Complexity: O(N^2)
// input: S = sequence from field K
// return: L          = degree of minimal polynomial,
//         C_reversed = monic min. polynomial (size = L + 1, reversed order, C_reversed[0] = 1))
// Formula: convolve(S, C_reversed)[i] = 0 for i >= L
// Example:
// - [1, 2, 4, 8, 16]   -> (1, [1, -2])
// - [1, 1, 2, 3, 5, 8] -> (2, [1, -1, -1])
// - [0, 0, 0, 0, 1]    -> (5, [1, 0, 0, 0, 0, 998244352]) (mod 998244353)
// - []                 -> (0, [1])
// - [0, 0, 0]          -> (0, [1])
// - [-2]               -> (1, [1, 2])
template <typename K>
std::pair<int, std::vector<K>> linear_recurrence(const std::vector<K> &S)
{
    int N = S.size();
    using poly = std::vector<K>;
    poly C_reversed{1}, B{1};
    int L = 0, m = 1;
    K b = 1;

    // adjust: C(x) <- C(x) - (d / b) x^m B(x)
    auto adjust = [](poly C, const poly &B, K d, K b, int m) -> poly {
        C.resize(std::max(C.size(), B.size() + m));
        K a = d / b;
        for (unsigned i = 0; i < B.size(); i++) C[i + m] -= a * B[i];
        return C;
    };

    for (int n = 0; n < N; n++) {
        K d = S[n];
        for (int i = 1; i <= L; i++) d += C_reversed[i] * S[n - i];

        if (d == 0) m++;
        else if (2 * L <= n) {
            poly T = C_reversed;
            C_reversed = adjust(C_reversed, B, d, b, m);
            L = n + 1 - L;
            B = T;
            b = d;
            m = 1;
        }
        else C_reversed = adjust(C_reversed, B, d, b, m++);
    }
    return std::make_pair(L, C_reversed);
}


// Calculate x^N mod f(x)
// Known as `Kitamasa method`
// Input: f_reversed: monic, reversed (f_reversed[0] = 1)
// Complexity: O(K^2 lgN) (K: deg. of f)
// Example: (4, [1, -1, -1]) -> [2, 3]
//          ( x^4 = (x^2 + x + 2)(x^2 - x - 1) + 3x + 2 )
// Reference: <http://misawa.github.io/others/fast_kitamasa_method.html>
//            <http://sugarknri.hatenablog.com/entry/2017/11/18/233936>
template <typename _Tfield>
std::vector<_Tfield> monomial_mod_polynomial(long long N, const std::vector<_Tfield> &f_reversed)
{
    assert(!f_reversed.empty() and f_reversed[0] == 1);
    int K = f_reversed.size() - 1;
    if (!K) return {};
    int D = 64 - __builtin_clzll(N);
    std::vector<_Tfield> ret(K, 0);
    ret[0] = 1;
    auto self_conv = [](std::vector<_Tfield> x) -> std::vector<_Tfield> {
        int d = x.size();
        std::vector<_Tfield> ret(d * 2 - 1);
        for (int i = 0; i < d; i++)
        {
            ret[i * 2] += x[i] * x[i];
            for (int j = 0; j < i; j++) ret[i + j] += x[i] * x[j] * 2;
        }
        return ret;
    };
    for (int d = D; d--;)
    {
        ret = self_conv(ret);
        for (int i = 2 * K - 2; i >= K; i--)
        {
            for (int j = 1; j <= K; j++) ret[i - j] -= ret[i] * f_reversed[j];
        }
        ret.resize(K);
        if ((N >> d) & 1)
        {
            std::vector<_Tfield> c(K);
            c[0] = -ret[K - 1] * f_reversed[K];
            for (int i = 1; i < K; i++)
            {
                c[i] = ret[i - 1] - ret[K - 1] * f_reversed[K - i];
            }
            ret = c;
        }
    }
    return ret;
}

// #include "modulus/modint_fixed.hpp"
#pragma once
#include <iostream>
#include <vector>
#include <set>

// CUT begin
template <int mod>
struct ModInt
{
    using lint = long long;
    static int get_mod() { return mod; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&](){
                std::set<int> fac;
                int v = mod - 1;
                for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < mod; g++) {
                    bool ok = true;
                    for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    constexpr ModInt() : val(0) {}
    constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
    constexpr ModInt(lint v) { _setval(v % mod + mod); }
    explicit operator bool() const { return val != 0; }
    constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    constexpr bool operator==(const ModInt &x) const { return val == x.val; }
    constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
    bool operator<(const ModInt &x) const { return val < x.val; }  // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
    friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val;  return os; }
    constexpr lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % mod;
            tmp = tmp * tmp % mod;
            n /= 2;
        }
        return ans;
    }
    constexpr lint inv() const { return this->power(mod - 2); }
    constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
    constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }

    inline ModInt fac() const {
        static std::vector<ModInt> facs;
        int l0 = facs.size();
        if (l0 > this->val) return facs[this->val];

        facs.resize(this->val + 1);
        for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
        return facs[this->val];
    }

    ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
        else return ModInt(k).fac() * ModInt(2).power(k);
    }

    ModInt nCr(const ModInt &r) const {
        if (this->val < r.val) return ModInt(0);
        return this->fac() / ((*this - r).fac() * r.fac());
    }

    ModInt sqrt() const {
        if (val == 0) return 0;
        if (mod == 2) return val;
        if (power((mod - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.power((mod - 1) / 2) == 1) b += 1;
        int e = 0, m = mod - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.power(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.power(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val, mod - x.val));
    }
};

// constexpr lint MOD = 998244353;
// using mint = ModInt<MOD>;

using mint = ModInt<1000000007>;
// #include "formal_power_series/formal_power_series.hpp"
#include <algorithm>
#include <array>
#include <cassert>
#include <vector>
using namespace std;

// CUT begin
// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
vector<MODINT> nttconv(vector<MODINT> a, vector<MODINT> b, bool skip_garner = false);

constexpr int nttprimes[3] = {998244353, 167772161, 469762049};

// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT>
void ntt(vector<MODINT> &a, bool is_inverse = false)
{
    int n = a.size();
    assert(__builtin_popcount(n) == 1);
    MODINT h = MODINT(MODINT::get_primitive_root()).power((MODINT::get_mod() - 1) / n);
    if (is_inverse) h = 1 / h;

    int i = 0;
    for (int j = 1; j < n - 1; j++) {
        for (int k = n >> 1; k > (i ^= k); k >>= 1);
        if (j < i) swap(a[i], a[j]);
    }

    for (int m = 1; m < n; m *= 2) {
        int m2 = 2 * m;
        long long int base = h.power(n / m2);
        MODINT w(1);
        for(int x = 0; x < m; x++) {
            for (int s = x; s < n; s += m2) {
                MODINT u = a[s], d = a[s + m] * w;
                a[s] = u + d, a[s + m] = u - d;
            }
            w *= base;
        }
    }
    if (is_inverse) {
        long long int n_inv = MODINT(n).inv();
        for (auto &v : a) v *= n_inv;
    }
}
template<int MOD>
vector<ModInt<MOD>> nttconv_(const vector<int> &a, const vector<int> &b) {
    int sz = a.size();
    assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
    vector<ModInt<MOD>> ap(sz), bp(sz);
    for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
    if (a == b) {
        ntt(ap, false);
        bp = ap;
    }
    else {
        ntt(ap, false);
        ntt(bp, false);
    }
    for (int i = 0; i < sz; i++) ap[i] *= bp[i];
    ntt(ap, true);
    return ap;
}
long long int extgcd_ntt_(long long int a, long long int b, long long int &x, long long int &y)
{
    long long int d = a;
    if (b != 0) d = extgcd_ntt_(b, a % b, y, x), y -= (a / b) * x;
    else x = 1, y = 0;
    return d;
}
long long int modinv_ntt_(long long int a, long long int m)
{
    long long int x, y;
    extgcd_ntt_(a, m, x, y);
    return (m + x % m) % m;
}
long long int garner_ntt_(int r0, int r1, int r2, int mod)
{
    array<long long int, 4> rs = {r0, r1, r2, 0};
    vector<long long int> coffs(4, 1), constants(4, 0);
    for (int i = 0; i < 3; i++) {
        long long int v = (rs[i] - constants[i]) * modinv_ntt_(coffs[i], nttprimes[i]) % nttprimes[i];
        if (v < 0) v += nttprimes[i];
        for (int j = i + 1; j < 4; j++) {
            (constants[j] += coffs[j] * v) %= (j < 3 ? nttprimes[j] : mod);
            (coffs[j] *= nttprimes[i]) %= (j < 3 ? nttprimes[j] : mod);
        }
    }
    return constants.back();
}
template <typename MODINT>
vector<MODINT> nttconv(vector<MODINT> a, vector<MODINT> b, bool skip_garner)
{
    int sz = 1, n = a.size(), m = b.size();
    while (sz < n + m) sz <<= 1;
    int mod = MODINT::get_mod();
    if (skip_garner or find(begin(nttprimes), end(nttprimes), mod) != end(nttprimes)) {
        a.resize(sz), b.resize(sz);
        if (a == b) { ntt(a, false); b = a; }
        else ntt(a, false), ntt(b, false);
        for (int i = 0; i < sz; i++) a[i] *= b[i];
        ntt(a, true);
        a.resize(n + m - 1);
    }
    else {
        vector<int> ai(sz), bi(sz);
        for (int i = 0; i < n; i++) ai[i] = a[i].val;
        for (int i = 0; i < m; i++) bi[i] = b[i].val;
        auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
        auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
        auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
        a.resize(n + m - 1);
        for (int i = 0; i < n + m - 1; i++) {
            a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod);
        }
    }
    return a;
}

#pragma once
// #include "convolution/ntt.hpp"
#include <algorithm>
#include <cassert>
#include <vector>
using namespace std;

// CUT begin
// Formal Power Series (形式的冪級数) based on ModInt<mod> / ModIntRuntime
// Reference: <https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.html>
template<typename T>
struct FormalPowerSeries : vector<T>
{
    using vector<T>::vector;
    using P = FormalPowerSeries;

    void shrink() { while (this->size() and this->back() == T(0)) this->pop_back(); }

    P operator+(const P &r) const { return P(*this) += r; }
    P operator+(const T &v) const { return P(*this) += v; }
    P operator-(const P &r) const { return P(*this) -= r; }
    P operator-(const T &v) const { return P(*this) -= v; }
    P operator*(const P &r) const { return P(*this) *= r; }
    P operator*(const T &v) const { return P(*this) *= v; }
    P operator/(const P &r) const { return P(*this) /= r; }
    P operator/(const T &v) const { return P(*this) /= v; }
    P operator%(const P &r) const { return P(*this) %= r; }

    P &operator+=(const P &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
        shrink();
        return *this;
    }
    P &operator+=(const T &v) {
        if (this->empty()) this->resize(1);
        (*this)[0] += v;
        shrink();
        return *this;
    }
    P &operator-=(const P &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
        shrink();
        return *this;
    }
    P &operator-=(const T &v) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= v;
        shrink();
        return *this;
    }
    P &operator*=(const T &v) {
        for (auto &x : (*this)) x *= v;
        shrink();
        return *this;
    }
    P &operator*=(const P &r) {
        if (this->empty() || r.empty()) this->clear();
        else {
            auto ret = nttconv(*this, r);
            *this = P(ret.begin(), ret.end());
        }
        return *this;
    }
    P &operator%=(const P &r) {
        *this -= *this / r * r;
        shrink();
        return *this;
    }
    P operator-() const {
        P ret = *this;
        for (auto &v : ret) v = -v;
        return ret;
    }
    P &operator/=(const T &v) {
        assert(v != T(0));
        for (auto &x : (*this)) x /= v;
        return *this;
    }
    P &operator/=(const P &r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = (int)this->size() - r.size() + 1;
        return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);
    }
    P pre(int sz) const {
         P ret(this->begin(), this->begin() + min((int)this->size(), sz));
         ret.shrink();
         return ret;
    }
    P operator>>(int sz) const {
        if ((int)this->size() <= sz) return {};
        return P(this->begin() + sz, this->end());
    }
    P operator<<(int sz) const {
        if (this->empty()) return {};
        P ret(*this);
        ret.insert(ret.begin(), sz, T(0));
        return ret;
    }

    P reversed(int deg = -1) const {
        assert(deg >= -1);
        P ret(*this);
        if (deg != -1) ret.resize(deg, T(0));
        reverse(ret.begin(), ret.end());
        ret.shrink();
        return ret;
    }

    P differential() const { // formal derivative (differential) of f.p.s.
        const int n = (int)this->size();
        P ret(max(0, n - 1));
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
        return ret;
    }

    P integral() const {
        const int n = (int)this->size();
        P ret(n + 1);
        ret[0] = T(0);
        for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
        return ret;
    }

    P inv(int deg) const {
        assert(deg >= -1);
        assert(this->size() and ((*this)[0]) != T(0)); // Requirement: F(0) != 0
        const int n = this->size();
        if (deg == -1) deg = n;
        P ret({T(1) / (*this)[0]});
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
        }
        ret = ret.pre(deg);
        ret.shrink();
        return ret;
    }

    P log(int deg = -1) const {
        assert(deg >= -1);
        assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1
        const int n = (int)this->size();
        if (deg == 0) return {};
        if (deg == -1) deg = n;
        return (this->differential() * this->inv(deg)).pre(deg - 1).integral();
    }

    P sqrt(int deg = -1) const {
        assert(deg >= -1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (this->empty()) return {};
        if ((*this)[0] == T(0)) {
            for (int i = 1; i < n; i++) if ((*this)[i] != T(0)) {
                if ((i & 1) or deg - i / 2 <= 0) return {};
                return (*this >> i).sqrt(deg - i / 2) << (i / 2);
            }
            return {};
        }
        T sqrtf0 = (*this)[0].sqrt();
        if (sqrtf0 == T(0)) return {};

        P y = (*this) / (*this)[0], ret({T(1)});
        T inv2 = T(1) / T(2);
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2;
        }
        return ret.pre(deg) * sqrtf0;
    }

    P exp(int deg = -1) const {
        assert(deg >= -1);
        assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        P ret({T(1)});
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
        }
        return ret.pre(deg);
    }

    P pow(long long int k, int deg = -1) const {
        assert(deg >= -1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != T(0)) {
                T rev = T(1) / (*this)[i];
                P C(*this * rev);
                P D(n - i);
                for (int j = i; j < n; j++) D[j - i] = C[j];
                D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].power(k);
                P E(deg);
                if (k * (i > 0) > deg or k * i > deg) return {};
                long long int S = i * k;
                for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];
                E.shrink();
                return E;
            }
        }
        return *this;
    }

    T coeff(int i) const {
        if ((int)this->size() <= i) return T(0);
        return (*this)[i];
    }

    T eval(T x) const {
        T ret = 0, w = 1;
        for (auto &v : *this) ret += w * v, w *= x;
        return ret;
    }
};

#include <iostream>

#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

FormalPowerSeries<mint> gen_dp(std::vector<int> v, int n)
{
    vector<vector<mint>> dp(n + 1, vector<mint>(v.back() * n + 1));
    dp[0][0] = 1;
    for (auto x : v)
    {
        for (int i = n - 1; i >= 0; i--)
        {
            for (int j = 0; j < dp[i].size(); j++) if (dp[i][j])
            {
                for (int k = 1; i + k <= n; k++) dp[i + k][j + x * k] += dp[i][j];
            }
        }
    }
    FormalPowerSeries<mint> ret(v.back() * n + 1, 0);
    for (int i = 0; i < ret.size(); i++) ret[i] = dp[n][i];
    return ret;
}

int main()
{
    long long N;
    int P, C;
    std::cin >> N >> P >> C;
    FormalPowerSeries<mint> primes = gen_dp({2, 3, 5, 7, 11, 13}, P), composites = gen_dp({4, 6, 8, 9, 10, 12}, C);
    auto f_reversed = primes * composites;
    std::vector<mint> dp(f_reversed.size());
    dp[0] = 1;
    for (int i = 0; i < dp.size(); i++)
    {
        for (int j = 1; i + j < dp.size(); j++) dp[i + j] += dp[i] * f_reversed[j];
    }

    for (auto &x : f_reversed) x = -x;
    f_reversed[0] = 1;

    std::vector<mint> g(f_reversed.size() - 1);
    g[0] = 1;
    if (N > f_reversed.size())
    {
        long long d = N - f_reversed.size();
        N -= d;
        g = monomial_mod_polynomial<mint>(d, f_reversed);
    }

    auto prod_x = [&](std::vector<mint> v) -> std::vector<mint> {
        int K = v.size();
        std::vector<mint> c(K);
        c[0] = -v[K - 1] * f_reversed[K];
        for (int i = 1; i < K; i++)
        {
            c[i] = v[i - 1] - v[K - 1] * f_reversed[K - i];
        }
        return c;
    };
    mint acc = 0;
    for (int i = N; i < f_reversed.size(); i++) acc += f_reversed[i];
    mint ret = 0;
    while (N)
    {
        mint p = std::inner_product(g.begin(), g.end(), dp.begin(), mint(0));
        ret -= acc * p;
        g = prod_x(g);
        N--;
        acc += f_reversed[N];
    }
    cout << ret << '\n';
}