#include using namespace std; using ll = long long; #define all(A) A.begin(),A.end() using vll = vector; using vvll = vector; #define rep(i, n) for (int i = 0; i < (int)(n); i++) vvll G; #include using namespace atcoder; #define rep2(i, m, n) for (int i = (m); i < (n); ++i) #define rep(i, n) rep2(i, 0, n) #define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i) #define drep(i, n) drep2(i, n, 0) template struct FormalPowerSeries : vector { using vector::vector; using vector::operator=; using F = FormalPowerSeries; F operator-() const { F res(*this); for (auto& e : res) e = -e; return res; } F& operator*=(const T& g) { for (auto& e : *this) e *= g; return *this; } F& operator/=(const T& g) { assert(g != T(0)); *this *= g.inv(); return *this; } F& operator+=(const F& g) { int n = (*this).size(), m = g.size(); rep(i, min(n, m)) (*this)[i] += g[i]; return *this; } F& operator-=(const F& g) { int n = (*this).size(), m = g.size(); rep(i, min(n, m)) (*this)[i] -= g[i]; return *this; } F& operator<<=(const int d) { int n = (*this).size(); (*this).insert((*this).begin(), d, 0); (*this).resize(n); return *this; } F& operator>>=(const int d) { int n = (*this).size(); (*this).erase((*this).begin(), (*this).begin() + min(n, d)); (*this).resize(n); return *this; } F inv(int d = -1) const { int n = (*this).size(); assert(n != 0 && (*this)[0] != 0); if (d == -1) d = n; assert(d > 0); F res{ (*this)[0].inv() }; while (res.size() < d) { int m = size(res); F f(begin(*this), begin(*this) + min(n, 2 * m)); F r(res); f.resize(2 * m), internal::butterfly(f); r.resize(2 * m), internal::butterfly(r); rep(i, 2 * m) f[i] *= r[i]; internal::butterfly_inv(f); f.erase(f.begin(), f.begin() + m); f.resize(2 * m), internal::butterfly(f); rep(i, 2 * m) f[i] *= r[i]; internal::butterfly_inv(f); T iz = T(2 * m).inv(); iz *= -iz; rep(i, m) f[i] *= iz; res.insert(res.end(), f.begin(), f.begin() + m); } return { res.begin(), res.begin() + d }; } // fast: FMT-friendly modulus only F &operator*=(const F &g) { int n = (*this).size(); *this = convolution(*this, g); (*this).resize(n); return *this; } /* F &operator/=(const F &g) { int n = (*this).size(); *this = convolution(*this, g.inv(n)); (*this).resize(n); return *this; } */ /* // naive F &operator*=(const F &g) { int n = (*this).size(), m = g.size(); drep(i, n) { (*this)[i] *= g[0]; rep2(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j]; } return *this; } */ F &operator/=(const F &g) { assert(g[0] != T(0)); T ig0 = g[0].inv(); int n = (*this).size(), m = g.size(); rep(i, n) { rep2(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j]; (*this)[i] *= ig0; } return *this; } // sparse F& operator*=(vector> g) { int n = (*this).size(); auto [d, c] = g.front(); if (d == 0) g.erase(g.begin()); else c = 0; drep(i, n) { (*this)[i] *= c; for (auto& [j, b] : g) { if (j > i) break; (*this)[i] += (*this)[i - j] * b; } } return *this; } F& operator/=(vector> g) { int n = (*this).size(); auto [d, c] = g.front(); assert(d == 0 && c != T(0)); T ic = c.inv(); g.erase(g.begin()); rep(i, n) { for (auto& [j, b] : g) { if (j > i) break; (*this)[i] -= (*this)[i - j] * b; } (*this)[i] *= ic; } return *this; } // multiply and divide (1 + cz^d) void multiply(const int d, const T c) { int n = (*this).size(); if (c == T(1)) drep(i, n - d) (*this)[i + d] += (*this)[i]; else if (c == T(-1)) drep(i, n - d) (*this)[i + d] -= (*this)[i]; else drep(i, n - d) (*this)[i + d] += (*this)[i] * c; } void divide(const int d, const T c) { int n = (*this).size(); if (c == T(1)) rep(i, n - d) (*this)[i + d] -= (*this)[i]; else if (c == T(-1)) rep(i, n - d) (*this)[i + d] += (*this)[i]; else rep(i, n - d) (*this)[i + d] -= (*this)[i] * c; } T eval(const T& a) const { T x(1), res(0); for (auto e : *this) res += e * x, x *= a; return res; } F operator*(const T& g) const { return F(*this) *= g; } F operator/(const T& g) const { return F(*this) /= g; } F operator+(const F& g) const { return F(*this) += g; } F operator-(const F& g) const { return F(*this) -= g; } F operator<<(const int d) const { return F(*this) <<= d; } F operator>>(const int d) const { return F(*this) >>= d; } F operator*(const F& g) const { return F(*this) *= g; } F operator/(const F& g) const { return F(*this) /= g; } F operator*(vector> g) const { return F(*this) *= g; } F operator/(vector> g) const { return F(*this) /= g; } }; using mint = modint1000000007; using F = FormalPowerSeries; vector fact, factinv, inv; ll mod = 1e9 + 7; void prenCkModp(ll n) { fact.resize(n + 5); factinv.resize(n + 5); inv.resize(n + 5); fact.at(0) = fact.at(1) = 1; factinv.at(0) = factinv.at(1) = 1; inv.at(1) = 1; for (ll i = 2; i < n + 5; i++) { fact.at(i) = (fact.at(i - 1) * i) % mod; inv.at(i) = mod - (inv.at(mod % i) * (mod / i)) % mod; factinv.at(i) = (factinv.at(i - 1) * inv.at(i)) % mod; } } ll nCk(ll n, ll k) { if (n < k) return 0; return fact.at(n) * (factinv.at(k) * factinv.at(n - k) % mod) % mod; } int main() { ll N, K; cin >> N >> K; F f = { 1 }; f.resize(N * N); rep(i, N) { f.multiply(i + 1, -1); f.divide(1, -1); } f.divide(1, -1); cout << f[K].val() << endl; }