#include using namespace std; /*#include #include using namespace __gnu_pbds; template using gpp_set = tree, rb_tree_tag, tree_order_statistics_node_update>; template using gpp_map = tree, rb_tree_tag, tree_order_statistics_node_update>; template using gpp_multiset = tree, rb_tree_tag, tree_order_statistics_node_update>;*/ struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define FOR(i, begin, end) for(int i=(begin);i<(end);i++) #define REP(i, n) FOR(i,0,n) #define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--) #define IREP(i, n) IFOR(i,0,n) #define Sort(v) sort(v.begin(), v.end()) #define Reverse(v) reverse(v.begin(), v.end()) #define all(v) v.begin(),v.end() #define SZ(v) ((int)v.size()) #define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x)) #define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x)) #define Max(a, b) a = max(a, b) #define Min(a, b) a = min(a, b) #define bit(n) (1LL<<(n)) #define bit_exist(x, n) ((x >> n) & 1) #define debug(x) cout << #x << "=" << x << endl; #define vdebug(v) { cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl; } #define mdebug(m) { cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;} } #define Return(ans) { cout << (ans) << endl; return 0; } #define pb push_back #define f first #define s second #define int long long #define INF 1000000000000000000 template istream &operator>>(istream &is, vector &v){ for (auto &x : v) is >> x; return is; } template ostream &operator<<(ostream &os, vector &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; } template ostream &operator<<(ostream &os, pair p){ cout << '(' << p.first << ',' << p.second << ')'; return os; } template void Out(T x) { cout << x << endl; } template void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); } using vec = vector; using mat = vector; using Pii = pair; using PiP = pair; using PPi = pair; using Pdi = pair; using bools = vector; using pairs = vector; //int dx[4] = {1,0,-1,0}; //int dy[4] = {0,1,0,-1}; //char d[4] = {'D','R','U','L'}; const int mod = 1000000007; //const int mod = 998244353; //#define Add(x, y) x = (x + (y)) % mod //#define Mult(x, y) x = (x * (y)) % mod template struct ModInt{ using ll = long long; ll val; void setval(ll v) { val = v % MOD; }; ModInt(): val(0) {} ModInt(ll v) { setval(v); }; ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); } ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); } ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); } ModInt operator/(const ModInt &x) const { return *this * x.inv(); } ModInt operator-() const { return ModInt(MOD - val); } ModInt operator+=(const ModInt &x) { return *this = *this + x; } ModInt operator-=(const ModInt &x) { return *this = *this - x; } ModInt operator*=(const ModInt &x) { return *this = *this * x; } ModInt operator/=(const ModInt &x) { return *this = *this / x; } friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; } friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; } ModInt pow(ll n) const { ModInt a = 1; if(n == 0) return a; int i0 = 64 - __builtin_clzll(n); for(int i = i0 - 1; i >= 0; i--){ a = a * a; if((n >> i) & 1) a *= (*this); } return a; } ModInt inv() const { return this->pow(MOD - 2); } }; using mint = ModInt; mint pow(mint x, long long n) { return x.pow(n); } //using mint = double; //for debug using mvec = vector; using mmat = vector; struct Combination{ vector fact, invfact; Combination(int N){ fact = vector({mint(1)}); invfact = vector({mint(1)}); fact_initialize(N); } void fact_initialize(int N){ int i0 = fact.size(); if(i0 >= N + 1) return; fact.resize(N + 1); invfact.resize(N + 1); for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i; invfact[N] = (mint)1 / fact[N]; for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); } mint nCr(int n, int r){ if(n < 0 || r < 0 || r > n) return mint(0); if(fact.size() < n + 1) fact_initialize(n); return fact[n] * invfact[r] * invfact[n - r]; } mint nPr(int n, int r){ if(n < 0 || r < 0 || r > n) return mint(0); if(fact.size() < n + 1) fact_initialize(n); return fact[n] * invfact[n - r]; } mint Catalan(int n){ if(n < 0) return 0; else if(n == 0) return 1; if(fact.size() < 2 * n + 1) fact_initialize(2 * n); return fact[2 * n] * invfact[n + 1] * invfact[n]; } }; template struct Matrix{ int R, C; vector element; __inline__ T &at(int i, int j) { return element[i * C + j]; } Matrix(int R, int C, vector &element): R(R), C(C), element(element) { assert(element.size() == R * C); } Matrix(vector> &_element) { R = _element.size(); C = _element[0].size(); element.resize(R * C); for(int i = 0; i < R; i++) for(int j = 0; j < C; j++) element[i * C + j] = _element[i][j]; } Matrix(int R, int C): R(R), C(C) { element = vector(R * C, (T)0); } //Make an identity matrix Matrix(int N): R(N), C(N) { element = vector(N * N, (T)0); for(int i = 0; i < N; i++) element[(N + 1) * i] = (T)1; } Matrix() :R(0), C(0) {} Matrix operator+(Matrix &x) { assert(R == x.R && C == x.C); Matrix M(R, C); for(int i = 0; i < R * C; i++) M.element[i] = element[i] + x.element[i]; return M; } Matrix operator-(Matrix &x) { assert(R == x.R && C == x.C); Matrix M(R, C); for(int i = 0; i < R * C; i++) M.element[i] = element[i] - x.element[i]; return M; } Matrix operator*(Matrix &x) { assert(C == x.R); Matrix M(R, x.C); for(int i = 0; i < R; i++) for(int j = 0; j < x.C; j++){ for(int k = 0; k < C; k++) M.at(i, j) += at(i, k) * x.at(k, j); } return M; } Matrix operator*(const T &a) { Matrix M(R, C); for(int i = 0; i < R * C; i++) M.element[i] = element[i] * a; return M; } Matrix operator+=(Matrix &x) { return *this = *this + x; } Matrix operator-=(Matrix &x) { return *this = *this - x; } Matrix operator*=(Matrix &x) { return *this = *this * x; } Matrix operator*=(const T &a) { for(int i = 0; i < R * C; i++) element[i] *= a; return *this; } Matrix pow(long long n) { assert(R == C); Matrix M(R); if(n == 0) return M; int i0 = 64 - __builtin_clzll(n); for(int i = i0 - 1; i >= 0; i--){ M *= M; if((n >> i) & 1) M *= (*this); } return M; } void Print(){ for(int i = 0; i < R; i++){ for(int j = 0; j < C; j++) cout << element[i * C + j] << " "; cout << endl; } } }; signed main(){ int M, K; cin >> M >> K; mmat A(M, mvec(M, 0)); REP(i, M){ REP(j, M){ A[i][(i + j) % M] += 1; A[i][(i * j) % M] += 1; } } Matrix a(A); mint ans = a.pow(K).at(0, 0); Out(ans); return 0; }