constexpr int mod = 1e9 + 7;
template <typename T>
T inv(T a, T m) {
    T u = 0, v = 1;
    while (a != 0) {
        T t = m / a;
        swap(a, m -= t * a);
        swap(u -= t * v, v);
    }
    assert(m == 1);
    return u;
}
struct modint {
    int n;
    modint() : n(0) {}
    modint(long long m) {
        if (m < 0 || mod <= m) {
            m %= mod;
            if (m < 0) m += mod;
        }
        n = m;
    }
    operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) {
    a.n += b.n;
    if (a.n >= mod) a.n -= mod;
    return a;
}
modint operator-=(modint& a, modint b) {
    a.n -= b.n;
    if (a.n < 0) a.n += mod;
    return a;
}
modint operator*=(modint& a, modint b) {
    a.n = (static_cast<long long>(a.n) * b.n) % mod;
    return a;
}
modint operator/=(modint& a, modint b) { return a *= modint(inv(b.n, mod)); }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator/(modint a, modint b) { return a /= b; }
template <typename T>
modint qpow(const modint& a, const T& b) {
    assert(b >= 0);
    modint x = a, res = 1;
    T p = b;
    while (p > 0) {
        if (p & 1) res *= x;
        x *= x;
        p >>= 1;
    }
    return res;
}

struct Fact {
    vector<modint> fact, factinv;
    int n;
    Fact(int _n) : n(_n), fact(_n + 1), factinv(_n + 1) {
        fact[0] = modint(1);
        for (int i = 0; i < n - 1; i++) fact[i + 1] = fact[i] * modint(i + 1);
        factinv[n - 1] = modint(1) / fact[n - 1];
        for (int i = n - 2; i >= 0; i--) factinv[i] = factinv[i + 1] * modint(i + 1);
    }
    modint C(int n, int k) {
        if (n < 0 || k < 0 || n < k) return 0;
        return fact[n] * factinv[k] * factinv[n - k];
    }
    modint A(int n, int k) {
        if (n < 0 || k < 0 || n < k) return 0;
        return fact[n] * factinv[n - k];
    }
};

template <typename T>
T inv(T a, T m) {
    T u = 0, v = 1;
    while (a != 0) {
        T t = m / a;
        swap(a, m-= t * a);
        swap(u-= t * v, v);
    }
    assert(m == 1);
    return u;
}

template <typename T>
class Modular {
public:
    using Type = typename decay<decltype(T::value)>::type;

    constexpr Modular() : value() {}
    template <typename U> Modular(const U& x) { value = normalize(x); }

    template <typename U>
    static Type normalize(const U& x) {
        Type v = static_cast<Type>((-mod() <= x && x < mod()) ? x : x % mod());
        if (v < 0) v += mod();
        return v;
    }

    const Type& operator()() const { return value; }
    template <typename U> explicit operator U() const { return static_cast<U>(value); }
    constexpr static Type mod() { return T::value; }

    Modular& operator+=(const Modular& other) {
        if ((value += other.value) >= mod()) value -= mod();
        return *this;
    }
    Modular& operator-=(const Modular& other) {
        if ((value -= other.value) < 0) value += mod();
        return *this;
    }
    template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
    template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
    Modular& operator++() { return *this += 1; }
    Modular& operator--() { return *this -= 1; }
    Modular operator++(int) {
        Modular result(*this);
        *this += 1;
        return result;
    }
    Modular operator--(int) {
        Modular result(*this);
        *this -= 1;
        return result;
    }
    Modular operator-() const { return Modular(-value); }

    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
        uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
        uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
        asm(
            "divl %4; \n\t"
            : "=a"(d), "=d"(m)
            : "d"(xh), "a"(xl), "r"(mod()));
        value = m;
#else
        value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
        return *this;
    }
    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
        long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
        value = normalize(value * rhs.value - q * mod());
        return *this;
    }
    template <typename U = T>
    typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
        value = normalize(value * rhs.value);
        return *this;
    }

    Modular& operator/=(const Modular& other) { return *this *= Modular(inv(other.value, mod())); }

    friend const Type& abs(const Modular& x) { return x.value; }
    template <typename U> friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
    template <typename U> friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
    template <typename V, typename U> friend V& operator>>(V& stream, Modular<U>& number);

private:
    Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template <typename T, typename U>
Modular<T> qpow(const Modular<T>& a, const U& b) {
    assert(b >= 0);
    Modular<T> x = a, res = 1;
    U p = b;
    while (p > 0) {
        if (p & 1) res *= x;
        x *= x;
        p >>= 1;
    }
    return res;
}

template <typename T> bool IsZero(const Modular<T>& number) { return number() == 0; }
template <typename T> string to_string(const Modular<T>& number) { return to_string(number()); }

// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T> U& operator<<(U& stream, const Modular<T>& number) { return stream << number(); }

// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
    typename common_type<typename Modular<T>::Type, long long>::type x;
    stream >> x;
    number.value = Modular<T>::normalize(x);
    return stream;
}

// using ModType = int;
// struct VarMod { static ModType value; };
// ModType VarMod::value;
// ModType& md = VarMod::value;//(can change)
// using Mint = Modular<VarMod>;

constexpr int md = (int)1e9 + 7;  //模数
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

struct Fact {
    std::vector<Mint> fact, factinv;
    int n;
    Fact(int _n) : n(_n), fact(_n + 1), factinv(_n + 1) {
        fact[0] = Mint(1);
        for (int i = 0; i < n - 1; i++) fact[i + 1] = fact[i] * Mint(i + 1);
        factinv[n - 1] = Mint(1) / fact[n - 1];
        for (int i = n - 2; i >= 0; i--) factinv[i] = factinv[i + 1] * Mint(i + 1);
    }
    Mint C(int n, int k) {
        if (n < 0 || k < 0 || n < k) return 0;
        return fact[n] * factinv[k] * factinv[n - k];
    }
    Mint A(int n, int k) {
        if (n < 0 || k < 0 || n < k) return 0;
        return fact[n] * factinv[n - k];
    }
};