#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; template struct modint { private: unsigned int value; static constexpr int mod() {return m;} public: constexpr modint(const long long x = 0) noexcept { long long y = x; if(y < 0 || y >= mod()) { y %= mod(); if(y < 0) y += mod(); } value = (unsigned int)y; } constexpr unsigned int val() noexcept {return value;} constexpr modint &operator+=(const modint &other) noexcept { value += other.value; if(value >= mod()) value -= mod(); return *this; } constexpr modint &operator-=(const modint &other) noexcept { unsigned int x = value; if(x < other.value) x += mod(); x -= other.value; value = x; return *this; } constexpr modint &operator*=(const modint &other) noexcept { unsigned long long x = value; x *= other.value; value = (unsigned int) (x % mod()); return *this; } constexpr modint &operator/=(const modint &other) noexcept { return *this *= other.inverse(); } constexpr modint inverse() const noexcept { assert(value); long long a = value,b = mod(),x = 1,y = 0; while(b) { long long q = a/b; a -= q*b; swap(a,b); x -= q*y; swap(x,y); } return modint(x); } constexpr modint power(long long N) const noexcept { assert(N >= 0); modint p = *this,ret = 1; while(N) { if(N & 1) ret *= p; p *= p; N >>= 1; } return ret; } constexpr modint operator+() {return *this;} constexpr modint operator-() {return modint() - *this;} constexpr modint &operator++(int) noexcept {return *this += 1;} constexpr modint &operator--(int) noexcept {return *this -= 1;} friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;} friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;} friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;} friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;} friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;} }; //using mint = modint<998244353>; using mint = modint<1000000007>; template struct mat { private: vector> m; int h,w; public: constexpr mat(int _h,int _w,T x = 0) noexcept {m.assign(_h,vector(_w,x));h = _h,w = _w;} constexpr vector operator[](const int i) const {assert(0 <= i && i < h); return m[i];} constexpr vector &operator[](const int i) noexcept {assert(0 <= i && i < h); return m[i];} constexpr mat operator+(mat &other) noexcept { mat tmp = *this; return tmp += other; } constexpr mat operator-(mat &other) noexcept { mat tmp = *this; return tmp -= other; } constexpr mat operator*(mat &other) noexcept { mat tmp = *this; return tmp *= other; } constexpr mat &operator+=(mat &other) noexcept { assert(h == other.h && w == other.w); for(int i = 0;i < h;i++)for(int j = 0;j < w;j++) m[i][j] += other[i][j]; return *this; } constexpr mat &operator-=(mat &other) noexcept { assert(h == other.h && w == other.w); for(int i = 0;i < h;i++)for(int j = 0;j < w;j++) m[i][j] -= other[i][j]; return *this; } constexpr mat &operator*=(mat &other) noexcept { assert(w == other.h); mat tmp(h,other.w); for(int i = 0;i < h;i++)for(int j = 0;j < other.w;j++)for(int k = 0;k < w;k++) tmp[i][j] += m[i][k]*other[k][j]; for(int i = 0;i < h;i++) { m[i].resize(other.w); for(int j = 0;j < other.w;j++) m[i][j] = tmp[i][j]; } return *this; } constexpr mat power(long n) noexcept { assert(h == w); assert(n >= 0); mat res(h,w); for(int i = 0;i < h;i++) res[i][i] = 1; mat p = *this; long ex = n; while(ex) { if(ex & 1) res *= p; p *= p; ex >>= 1; } return res; } constexpr bool operator==(mat &other) noexcept { assert(h == other.h && w == other.w); bool res = true; for(int i = 0;i < h;i++)for(int j = 0;j < w;j++) if(m[i][j] != other[i][j]) res = false; return res; } constexpr bool operator!=(mat &other) noexcept { assert(h == other.h && w == other.w); bool res = false; for(int i = 0;i < h;i++)for(int j = 0;j < w;j++) if(m[i][j] != other[i][j]) res = true; return res; } template friend ostream &operator<<(ostream &os,const mat &x); }; template ostream &operator<<(ostream &os,const mat &x) { for(int i = 0;i < x.h;i++)for(int j = 0;j < x.w;j++) { os << x[i][j] << (j+1 == x.w && i+1 < x.h ? "\n":" "); return os; } } int M,K; void solve() { cin >> M >> K; mat MAT(M,M); for(int i = 0;i < M;i++) { for(int j = 0;j < M;j++) { int k = (i+j)%M; MAT[k][i]++; k = i*j%M; MAT[k][i]++; } } mat S(M,1); S[0][0] = 1; mat MS = MAT.power(K) * S; cout << MS[0][0] << endl; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int tt = 1; //cin >> tt; while(tt--) solve(); }