//header #ifdef LOCAL #include "cxx-prettyprint-master/prettyprint.hpp" #define debug(x) cout << x << endl #else #define debug(...) 42 #endif #pragma GCC optimize("Ofast") #include //types using namespace std; using ll = long long; using ld = long double; typedef pair < ll , ll > Pl; typedef pair < int, int > Pi; typedef vector vl; typedef vector vi; template< typename T > using mat = vector< vector< T > >; template< int mod > struct modint { int x; modint() : x(0) {} modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} modint &operator+=(const modint &p) { if((x += p.x) >= mod) x -= mod; return *this; } modint &operator-=(const modint &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } modint &operator*=(const modint &p) { x = (int) (1LL * x * p.x % mod); return *this; } modint &operator/=(const modint &p) { *this *= p.inverse(); return *this; } modint operator-() const { return modint(-x); } modint operator+(const modint &p) const { return modint(*this) += p; } modint operator-(const modint &p) const { return modint(*this) -= p; } modint operator*(const modint &p) const { return modint(*this) *= p; } modint operator/(const modint &p) const { return modint(*this) /= p; } bool operator==(const modint &p) const { return x == p.x; } bool operator!=(const modint &p) const { return x != p.x; } modint inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return modint(u); } modint pow(int64_t n) const { modint ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const modint &p) { return os << p.x; } friend istream &operator>>(istream &is, modint &a) { int64_t t; is >> t; a = modint< mod >(t); return (is); } static int get_mod() { return mod; } }; //abreviations #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define rep_(i, a_, b_, a, b, ...) for (int i = (a), max_i = (b); i < max_i; i++) #define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define rev(i,n) for(int i=n-1;i>=0;i--) #define SZ(x) ((int)(x).size()) #define pb(x) push_back(x) #define eb(x) emplace_back(x) #define mp make_pair #define print(x) cout << x << endl #define lsum(x) accumulate(x, 0LL) #define vmax(a) *max_element(all(a)) #define vmin(a) *min_element(all(a)) //functions ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; } ll lcm(ll a, ll b) { return a/gcd(a, b)*b;} templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b T mypow(T x, ll n) { T ret = 1; while(n > 0) { if(n & 1) (ret *= x); (x *= x); n >>= 1; } return ret; } ll modpow(ll x, ll n, const ll mod) { ll ret = 1; while(n > 0) { if(n & 1) (ret *= x); (x *= x); n >>= 1; x%=mod; ret%=mod; } return ret; } uint64_t my_rand(void) { static uint64_t x = 88172645463325252ULL; x = x ^ (x << 13); x = x ^ (x >> 7); return x = x ^ (x << 17); } //graph template template< typename T > struct edge { int src, to; T cost; edge(int to, T cost) : src(-1), to(to), cost(cost) {} edge(int src, int to, T cost) : src(src), to(to), cost(cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template< typename T > using Edges = vector< edge< T > >; template< typename T > using WeightedGraph = vector< Edges< T > >; //constant #define INF 4001002003004005006LL #define inf 1000000005 #define mod 1000000007LL #define endl '\n' typedef modint mint; const long double eps = 0.001; const long double PI = 3.141592653589793; //library template< class T > struct Matrix { vector< vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {} Matrix(size_t n) : A(n, vector< T >(n, 0)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector< T > &operator[](int k) const { return (A.at(k)); } inline vector< T > &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for(int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector< vector< T > > C(n, vector< T >(m, 0)); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) for(int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while(k > 0) { if(k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for(int i = 0; i < n; i++) { os << "["; for(int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for(int i = 0; i < width(); i++) { int idx = -1; for(int j = i; j < width(); j++) { if(B[j][i] != 0) idx = j; } if(idx == -1) return (0); if(i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for(int j = 0; j < width(); j++) { B[i][j] /= vv; } for(int j = i + 1; j < width(); j++) { T a = B[j][i]; for(int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; int main(){ cin.tie(0); ios::sync_with_stdio(0); cout << setprecision(20); ll m, k; cin>>m>>k; Matrix M(m, m); rep(s, m){ rep(i, m){ M[s][s*i%m]+=1; M[s][(s+i)%m]+=1; } } Matrix ans(m, m); rep(i, m)ans[i][i] = 1; while(k){ if(k&1){ ans*=M; } M*=M; k>>=1; } cout << ans[0][0] << endl; }