#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template<class T> using vec = vector<T>;
template<class T> using vvec = vector<vector<T>>;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
constexpr char ln = '\n';
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
    return os << "(" << p.first << ", " << p.second << ")";
}
template<class T> 
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    for (int i = 0; i < int(v.size()); i++) {
        if (i) os << ", ";
        os << v[i];
    }
    return os << "}";
}
template<class Container> inline int SZ(const Container& v) { return int(v.size()); }
template<class T> inline void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template<class T1, class T2> inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template<class T1, class T2> inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
inline int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
inline int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
inline int popcount(ull x) { return __builtin_popcountll(x); }
inline int kthbit(ull x, int k) { return (x >> k) & 1; }
inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x-1) * 10; }
template<class T> inline T ABS(T x) { return max(x, -x); }
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
const string yesno[2] = {"no", "yes"};
inline void YES(bool t = 1) { cout << YESNO[t] << "\n"; }
inline void Yes(bool t = 1) { cout << YesNo[t] << "\n"; }
inline void yes(bool t = 1) { cout << yesno[t] << "\n"; }
inline void print() { cout << "\n"; }
template<class T>
inline void print(const vector<T>& v) {
    for (auto it = begin(v); it != end(v); ++it) {
        if (it != begin(v)) cout << " ";
        cout << *it;
    }
    print();
}
template<class T, class... Args>
inline void print(const T& x, const Args& ... args) {
    cout << x << " ";
    print(args...);
}
#ifdef MINATO_LOCAL
inline void debug_out() { cerr << endl; }
template <class T, class... Args>
inline void debug_out(const T& x, const Args& ... args) {
    cerr << " " << x;
    debug_out(args...);
}
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); cerr << fixed << setprecision(7); }; } fast_ios_;
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////


#include <algorithm>
#include <array>
#include <cassert>
#include <type_traits>
#include <vector>


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

namespace atcoder {

namespace internal {

int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder


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

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


#include <utility>

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

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {

        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 int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

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;
}

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);

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};

    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


        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

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);

}  // namespace internal

}  // namespace atcoder


#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


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


namespace atcoder {

namespace internal {

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static bool first = true;
    static mint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[bsf(~(unsigned int)(s))];
        }
    }
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static bool first = true;
    static mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }

    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                    (unsigned long long)(mint::mod() + l.val() - r.val()) *
                    inow.val();
            }
            inow *= sum_ie[bsf(~(unsigned int)(s))];
        }
    }
}

}  // namespace internal

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) {
        if (n < m) {
            std::swap(n, m);
            std::swap(a, b);
        }
        std::vector<mint> ans(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
        return ans;
    }
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}

template <unsigned int mod = 998244353,
          class T,
          std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}

std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    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 constexpr unsigned long long i1 =
        internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
        internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
        internal::inv_gcd(MOD1 * MOD2, MOD3).second;

    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);

    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        long long diff =
            c1[i] - internal::safe_mod((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;
}

}  // namespace atcoder

using namespace atcoder;
//using mint = modint998244353;
using mint = modint1000000007;
//using mint = modint;

istream& operator>>(istream& is, modint998244353& M) { long long x; is >> x; M = x; return is; }
ostream& operator<<(ostream& os, const modint998244353& M) { return os << M.val(); }
istream& operator>>(istream& is, modint1000000007& M) { long long x; is >> x; M = x; return is; }
ostream& operator<<(ostream& os, const modint1000000007& M) { return os << M.val(); }
template<int m> istream& operator>>(istream& is, static_modint<m>& M) { long long x; is >> x; M = x; return is; }
template<int m> ostream& operator<<(ostream& os, const static_modint<m>& M) { return os << M.val(); }
istream& operator>>(istream& is, modint& M) { long long x; is >> x; M = x; return is; }
ostream& operator<<(ostream& os, const modint& M) { return os << M.val(); }

vector<mint> multiply(vector<mint> a, vector<mint> b) { return convolution(a,b); }
vector<mint> multiply_naive(vector<mint> a, vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    if (!n or !m) return {};
    vector<mint> ret(n + m - 1);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            ret[i + j] += a[i] * b[j];
        }
    }
    return ret;
}

//59501818244292734739283969=5.95*10^25 までの値を正しく計算
//最終的な列の大きさが 2^24 までなら動く
//最終的な列の大きさが 2^20 以下のときは，下の 3 つの素数を使ったほうが速い
namespace arbitrary_convolution {
    constexpr int m0 = 167772161;
    constexpr int m1 = 469762049;
    constexpr int m2 = 754974721;
    constexpr int r01 = 104391568; // mint1(m0).inv()
    constexpr int r02 = 323560596; // mint2(m0).inv()
    constexpr int r12 = 399692502; // mint2(m1).inv()
    // constexpr int m0 = 1045430273;
    // constexpr int m1 = 1051721729;
    // constexpr int m2 = 1053818881;
    // constexpr int r01 = 175287122; // mint1(m0).inv()
    // constexpr int r02 = 395182206; // mint2(m0).inv()
    // constexpr int r12 = 526909943; // mint2(m1).inv()
    constexpr int r02r12 = (long long)(r02) * r12 % m2;
    constexpr long long w1 = m0;
    constexpr long long w2 = (long long)(m0) * m1;

    template<class T>
    vector<int> multiply(const vector<T>& a, const vector<T>& b, int mod) {
        int n = int(a.size()), m = int(b.size());

        vector<T> v0 = convolution<m0>(a, b);
        vector<T> v1 = convolution<m1>(a, b);
        vector<T> v2 = convolution<m2>(a, b);
        vector<int> ret(n + m - 1);

        const int W1 = w1 % mod;
        const int W2 = w2 % mod;
        for (int i = 0; i < n + m - 1; i++) {
            int n1 = v1[i], n2 = v2[i], x = v0[i];
            int y = (long long)(n1 + m1 - x) * r01 % m1;
            int z = ((long long)(n2 + m2 - x) * r02r12 + (long long)(m2 - y) * r12) % m2;
            ret[i] = ((long long)(x) + (long long)(y) * W1 + (long long)(z) * W2) % mod;
        }
        return ret;
    }

    template<class D>
    vector<D> multiply(vector<D> a, vector<D> b) {
        int n = int(a.size()), m = int(b.size());
        if (!n or !m) return {};
        if (min(n,m) < 128) {
            if (n < m) {
                swap(n, m);
                swap(a, b);
            }
            vector<D> ret(n + m - 1);
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i + j] += a[i] * b[j];
                }
            }
            return ret;
        }
        vector<int> a_(n), b_(m);
        for (int i = 0; i < n; i++) a_[i] = a[i].val();
        for (int i = 0; i < m; i++) b_[i] = b[i].val();
        vector<int> c = multiply<int>(a_, b_, D::mod());
        vector<D> ret(n + m - 1);
        for (int i = 0; i < n + m - 1; i++) ret[i] = D::raw(c[i]);
        return ret;
    }
}

template<class D, vector<D> (*op)(vector<D>, vector<D>)> 
struct FormalPowerSeries {
    using Poly = FormalPowerSeries;

    vector<D> v;

    FormalPowerSeries(const vector<D>& v_ = {}) : v(v_) { shrink(); }
    void shrink() {
        while (v.size() && v.back() == 0) v.pop_back();
    }

    int size() const { return int(v.size()); }

    D freq(int p) const { return (p < size()) ? v[p] : D(0); }

    Poly operator+(const Poly& r) const {
        int n = max(size(), r.size());
        vector<D> res(n);
        for (int i = 0; i < n; i++) res[i] = freq(i) + r.freq(i);
        return res;
    }
    Poly operator-(const Poly& r) const {
        int n = max(size(), r.size());
        vector<D> res(n);
        for (int i = 0; i < n; i++) res[i] = freq(i) - r.freq(i);
        return res;
    }
    Poly operator*(const Poly& r) const { return op(v, r.v); }
    Poly operator*(const D& r) const {
        int n = size();
        vector<D> res(n);
        for (int i = 0; i < n; i++) res[i] = v[i] * r;
        return res;
    }
    Poly operator*(const vector<pair<int, D>>& r) const {
        assert(!r.empty());
        int n = size();
        int m = r.back().first;
        vector<D> res(n + m);
        for (int i = 0; i < n; i++) {
            for (auto e : r) {
                res[i + e.first] += v[i] * e.second;
            }
        }
        return res;
    }
    Poly operator/(const D& r) const {
        return *this * r.inv();
    }
    Poly operator/(const Poly& r) const {
        if (size() < r.size()) return {{}};
        int n = size() - r.size() + 1;
        return (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
    }
    Poly operator/(const vector<pair<int, D>>& r) const {
        assert(!r.empty());
        int n = size();
        auto [d, c] = r.front();
        assert(d == 0 && c != D(0));
        D ic = D(1) / c;
        vector<D> res(n);
        for (int i = 0; i < n; i++) {
            for (auto& e : r) {
                if (e.first and e.first <= i) {
                    res[i] -= res[i - e.first] * e.second;
                } 
            }
            res[i] += v[i];
            res[i] *= ic;
        }
        return res;
    }
    
    Poly operator%(const Poly& r) const { return *this - *this / r * r; }
    Poly operator<<(int s) const {
        vector<D> res(size() + s);
        for (int i = 0; i < size(); i++) res[i + s] = v[i];
        return res;
    }
    Poly operator>>(int s) const {
        if (size() <= s) return Poly();
        vector<D> res(size() - s);
        for (int i = 0; i < size() - s; i++) res[i] = v[i + s];
        return res;
    }
    Poly& operator+=(const Poly& r) { return *this = *this + r; }
    Poly& operator-=(const Poly& r) { return *this = *this - r; }
    Poly& operator*=(const Poly& r) { return *this = *this * r; }
    Poly& operator*=(const D& r) { return *this = *this * r; }
    Poly& operator*=(const vector<pair<int, D>>& r) { return *this = *this * r; }
    Poly& operator/=(const Poly& r) { return *this = *this / r; }
    Poly& operator/=(const D &r) {return *this = *this/r;}
    Poly& operator/=(const vector<pair<int, D>>& r) { return *this = *this / r; }
    Poly& operator%=(const Poly& r) { return *this = *this % r; }
    Poly& operator<<=(const size_t& n) { return *this = *this << n; }
    Poly& operator>>=(const size_t& n) { return *this = *this >> n; }

    Poly mul(int d, const D& c) const {
        vector<D> res(size() + d);
        for (int i = 0; i < size(); i++) {
            res[i] += v[i];
            res[i+d] += v[i] * c;
        }
        return res;
    }
    Poly div(int d, const D& c) const {
        vector<D> res(size());
        for (int i = 0; i < size(); i++) {
            res[i] = v[i];
            if (i >= d) res[i] -= res[i - d] * c;
        }
        return res;
    }
    Poly pre(int le) const {
        return {{v.begin(), v.begin() + min(size(), le)}};
    }
    Poly rev(int n = -1) const {
        vector<D> res = v;
        if (n != -1) res.resize(n);
        reverse(res.begin(), res.end());
        return res;
    }
    Poly diff() const {
        vector<D> res(max(0, size() - 1));
        for (int i = 1; i < size(); i++) res[i - 1] = freq(i) * i;
        return res;
    }
    Poly inte() const {
        vector<D> res(size() + 1);
        for (int i = 0; i < size(); i++) res[i + 1] = freq(i) / (i + 1);
        return res;
    }

    // f * f.inv() = 1 + g(x)x^m
    Poly inv(int m) const {
        Poly res = Poly({D(1) / freq(0)});
        for (int i = 1; i < m; i *= 2) {
            res = (res * D(2) - res * res * pre(2 * i)).pre(2 * i);
        }
        return res.pre(m);
    }
    Poly exp(int n) const {
        assert(freq(0) == 0);
        Poly f({1}), g({1});
        for (int i = 1; i < n; i *= 2) {
            g = (g * 2 - f * g * g).pre(i);
            Poly q = diff().pre(i - 1);
            Poly w = (q + g * (f.diff() - f * q)).pre(2 * i - 1);
            f = (f + f * (*this - w.inte()).pre(2 * i)).pre(2 * i);
        }
        return f.pre(n);
    }
    Poly log(int n) const {
        assert(freq(0) == 1);
        auto f = pre(n);
        return (f.diff() * f.inv(n - 1)).pre(n - 1).inte();
    }
    Poly sqrt(int n) const {
        assert(freq(0) == 1);
        Poly f = pre(n + 1);
        Poly g({1});
        for (int i = 1; i < n; i *= 2) {
            g = (g + f.pre(2 * i) * g.inv(2 * i)) / 2;
        }
        return g.pre(n + 1);
    }

    Poly pow_mod(ll n, const Poly& mod) {
        Poly x = *this, r = {{1}};
        while (n) {
            if (n & 1) r = r * x % mod;
            x = x * x % mod;
            n >>= 1;
        }
        return r;
    }

    friend ostream& operator<<(ostream& os, const Poly& p) {
        if (p.size() == 0) return os << "0";
        for (auto i = 0; i < p.size(); i++) {
            if (p.v[i] != 0) {
                os << p.v[i] << " x^" << i;
                if (i != p.size() - 1) os << " + ";
            }
        }
        return os;
    }
};

using Poly = FormalPowerSeries<mint, arbitrary_convolution::multiply>;

int main() {
    int K,N; cin >> K >> N;
    Poly f;
    f.v.assign(K+1,0);
    f.v[0] = 1;
    rep(i,N) {
        int x; cin >> x;
        if (x <= K) f.v[x]--;
    }
    f = f.inv(K+1);

    cout << f.freq(K) << ln;
}