#if !__INCLUDE_LEVEL__ #include __FILE__ vector lldiv(ll n) { vector S; for (ll i = 1; 1LL*i*i <= n; i++) if (n%i == 0) { S.push_back(i); if (i*i != n) S.push_back(n / i); } sort(S.begin(), S.end()); return S; } template struct Compress { vector xs; Compress() = default; Compress(const vector &vs) { add(vs); } Compress(const initializer_list> &vs) { for (auto &p : vs) add(p); } void add(const vector &vs) { copy(begin(vs), end(vs), back_inserter(xs)); } void add(const T &x) { xs.emplace_back(x); } void build() { sort(begin(xs), end(xs)); xs.erase(unique(begin(xs), end(xs)), end(xs)); } vector get(const vector &vs) const { vector ret; transform(begin(vs), end(vs), back_inserter(ret), [&](const T &x) { return lower_bound(begin(xs), end(xs), x) - begin(xs); }); return ret; } int get(const T &x) const { return lower_bound(begin(xs), end(xs), x) - begin(xs); } const T &operator[](int k) const { return xs[k]; } }; //行列の積 #define mat vector> const ll MOD = 1000000007; mat mat_mul(mat &a, mat &b) { mat res(a.size(), vector(b[0].size())); for (int i = 0; i < a.size(); i++) { for (int j = 0; j < b[0].size(); j++) { for (int k = 0; k < b.size(); k++) { (res[i][j] += a[i][k] * b[k][j]) %= MOD; } } } return res; } /// 行列累乗 mat mat_pow(mat a, long long n) { mat res(a.size(), vector(a.size())); // 単位行列で初期化 for (int i = 0; i < a.size(); i++)res[i][i] = 1; // 繰り返し二乗法 while (n > 0) { if (n & 1) res = mat_mul(a, res); a = mat_mul(a, a); n >>= 1; } return res; } int main() { ll N,M;cin >> N >> M; auto div = lldiv(M); Compress comp(div); comp.build(); ll D = div.size(); vector> DP(N+1,vector(D,0)); unordered_map Dflag; fore(d,div){ Dflag[d] = 1; DP[1][comp.get(d)] = 1; } vvl Mat(D,vl(D,0)); rep(j,D){ rep(k,D){ if(Dflag[div[j]*div[k]]==1){ Mat[j][k] = 1; } } } mat R = mat_pow(Mat,N-1); mat L(1,vl(D,1)); mat Ans(1,vl(N,0)); Ans = mat_mul(L,R); mint1 ans = 0; rep(d,D)ans += Ans[0][d]; cout << ans << endl; } #else #include #include using namespace std; using namespace atcoder; #define rep(i, n) for(int i = 0; i < n; i++) #define rrep(i, n) for(int i = n-1; i >= 0; i--) #define range(i, m, n) for(int i = m; i < n; i++) #define fore(i,a) for(auto &i:a) #define all(v) v.begin(), v.end() #define rall(v) v.rbegin(), v.rend() #define Sum(v) accumulate(all(v),0) #define minv(v) *min_element(all(v)) #define maxv(v) *max_element(all(v)) typedef long long ll; typedef vector vl; typedef vector> vvl; const ll INF = 1e16; const ll MOD1 = 1000000007; const ll MOD2 = 998244353; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } ll SN(char s){return ll(s-'0');} ll SN(string s){return stoll(s);} int alpN(char s){return int(s-'a');} int AlpN(char s){return int(s-'A');} using Graph = vector>; using GraphCost = vector>>; using mint1 = modint1000000007; using mint2 = modint998244353; using pll = pair; template ostream &operator<<(ostream &o,const vector&v){for(int i=0;i<(int)v.size();i++)o<<(i>0?" ":"")< bool contain(const std::string& s, const T& v) { return s.find(v) != std::string::npos; } #endif