#include "bits/stdc++.h" #include #include #include "atcoder/all" #include //#include //using namespace boost::multiprecision; // std::fixed << std::setprecision(10) << using namespace std; using namespace atcoder; using ll = long long; using ull = unsigned long long; using mint = modint998244353; using mint2 = modint1000000007; const double eps = 1e-9; #define REP(i, n) for (ll i = 0; i < ll(n); ++i) #define REPI(i, init, n) for (ll i = init; i < ll(n); ++i) #define REPD(i, init) for (ll i = init; i >=0; --i) #define REPDI(i, init, n) for (ll i = init; i >=n; --i) #define REPE(i, c) for (const auto& i : c) #define TCASE() ll _ttt; cin >> _ttt; while(_ttt--) using vl = vector; using vvl = vector; using vvvl = vector; #define VL(a, n) vector a; a.assign(n, 0); #define VLI(a, n) vector a; a.assign(n, 0); for(auto& x : a) cin >> x; #define VSI(a, n) vector a; a.assign(n, ""); for(auto& x : a) cin >> x; #define VVLI(a, n, m, init) vector> a(n); for(auto& x : a) x.assign(m, init); using vd = vector; using pl = pair; struct uv { ll u; ll v; ll c; }; #define VUVI(a, n) vector a; a.assign(n, {0, 0, 1}); for(auto& x : a) {cin >> x.u >> x.v; x.u--; x.v--;} #define VUVCI(a, n) vector a; a.assign(n, {0, 0, 0}); for(auto& x : a) {cin >> x.u >> x.v >> x.c; x.u--; x.v--;} vvl to_edge(const ll n, const vector& v) { vvl ret(n); for (auto& x : v) ret[x.u].push_back(x.v); return ret; } vvl to_edge_d(const ll n, const vector& v) { vvl ret(n); for (auto& x : v) { ret[x.u].push_back(x.v); ret[x.v].push_back(x.u); } return ret; } template using pql = priority_queue; template using pqg = priority_queue, greater>; using vm = vector; using vvm = vector; void yn(bool f) { std::cout << (f ? "Yes" : "No") << endl; }; template void ov(const T& v) { for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) cout << " "; cout << *it; } }; template<> void ov(const vm& v) { for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) cout << " "; cout << it->val(); } }; const ll llhuge = 1LL << 60; //十分でかいが多少足しても溢れない数値 auto gmax(const auto& a, const auto& b) { return a > b ? a : b; }; auto gmin(const auto& a, const auto& b) { return a < b ? a : b; }; bool chmin(auto& a, const auto& b) { const auto olda = a; a = gmin(a, b); return olda != a; } bool chmax(auto& a, const auto& b) { const auto olda = a; a = gmax(a, b); return olda != a; } template void mysort(T& v) { std::sort(begin(v), end(v)); }; template void mysort(T& v, U pr) { std::sort(begin(v), end(v), pr); }; template void myrev(T& v) { std::reverse(begin(v), end(v)); }; template [[nodiscard]] V myat(const T& mp, const K& key) { return mp.find(key) == mp.end() ? V() : mp.at(key); } long long ceil(const long long a, const long long b) { return (a + b - 1) / b; } //約数列挙(O(√n log √n)) //n<=10^6の時 size(result) <= 128 //n<=10^7の時 size(result) <= 240 //n<=10^8の時 size(result) <= 448 //n<=10^9の時 size(result) <= 768 //n<=10^10の時 size(result) <= 1344 vector divisor(long long n) { vector ret; for (long long i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i); if (i * i != n) ret.push_back(n / i); } } sort(ret.begin(), ret.end()); return ret; } using mat_row = vector; using mat = vector; mat make_mat(ll size, mint init = 0) { return mat(size, mat_row(size, init)); } mat operator*(const mat& a, const mat& b) { mat c(a.size(), mat_row(b[0].size())); for (size_t i = 0; i < c.size(); ++i) for (size_t j = 0; j < c[0].size(); ++j) for (size_t k = 0; k < a[0].size(); ++k) c[i][j] += a[i][k] * b[k][j]; return c; } mat pow(mat a, ll n) { mat res(a.size(), mat_row(a[0].size())); for (size_t i = 0; i < res.size(); ++i) res[i][i] = 1; for (; n; n /= 2) { if (n & 1) res = res * a; a = a * a; } return res; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << std::fixed << std::setprecision(10); ll n, m; cin >> n >> m; const vl divm = divisor(m); const int sz = divm.size(); map mp; for (int i = 0; i < divm.size(); i++) { mp[divm[i]] = i; } auto mt = make_mat(sz); REP(i, sz) { REP(j, sz) { mt[i][mp[lcm(divm[i], divm[j])]] += 1; } } auto mtp = pow(mt, n); cout << mtp[0][sz - 1].val() << endl; return 0; }