//#pragma GCC target("avx") //#pragma GCC optimize("Ofast") //#pragma GCC optimize("unroll-loops") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #include using namespace std; #include using namespace atcoder; //local debug #ifdef LOCAL #include #define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else #define debug(...) (static_cast(0)) #endif #define overload4(a, b, c, d, e, ...) e //alias using uint = unsigned int; using ll = long long; using ull = unsigned long long; using ld = long double; using mint = modint998244353; using Mint = modint1000000007; //constants constexpr const long long MOD = 998244353; constexpr const long long MODM = 1000000007; constexpr const int INF = 1e9; constexpr const ll LINF = 1e18; //rep(for-loop) macro #define rep2(i, n) for(ll i = 0; i < n; i++) #define rep3(i, k, n) for(ll i = k; i < n; i++) #define rep4(i, k, n, a) for(ll i = k; i < n; i += a) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2)(__VA_ARGS__) #define rep1_2(i, n) for(ll i = 1; i <= n; i++) #define rep1_3(i, k, n) for(ll i = k; i <= n; i++) #define rep1_4(i, k, n, a) for(ll i = k; i <= n; i += a) #define rep1(...) overload4(__VA_ARGS__, rep1_4, rep1_3, rep1_2)(__VA_ARGS__) #define Rep2(i, n) for(ll i = n - 1; i >= 0; i--) #define Rep3(i, k, n) for(ll i = n - 1; i >= k; i--) #define Rep4(i, k, n, a) for(ll i = n - 1; i >= k; i -= a) #define Rep(...) overload4(__VA_ARGS__, Rep4, Rep3, Rep2)(__VA_ARGS__) #define Rep1_2(i, n) for(ll i = n; i >= 1; i--) #define Rep1_3(i, k, n) for(ll i = n; i >= k; i--) #define Rep1_4(i, k, n, a) for(ll i = n; i >= k; i -= a) #define Rep1(...) overload4(__VA_ARGS__, Rep1_4, Rep1_3, Rep1_2)(__VA_ARGS__) #define vfor(v, x) for(auto x : v) #define mfor(map) for(auto &[key, value] : map) //vector macro #define vvecc(T, name, n, m) vector> name(n, vector(m)) #define vvec(T, name, n) vector> name(n) #define vvecs(T, name, n, m, s) vector> name(n, vector(m, s)) #define all(x) begin(x), end(x) #define LB(v, x) distance((v).begin(), lower_bound(all(v), (x))) #define UB(v, x) distance((v).begin(), upper_bound(all(v), (x))) //data structure macro #define ef emplace_front #define eb emplace_back #define pf pop_front #define pb pop_back #define mp make_pair #define fi first #define se second #define mt make_tuple #define get(t, x) get(t) #define lb lower_bound #define ub upper_bound template using pq = priority_queue; template using pqmin = priority_queue, greater>; template using pqp = priority_queue>; template using pqpmin = priority_queue, vector>, greater>>; //output #define pl() cout << '\n' template void print(const T& a) {cout << a;} void printl(){} template void printl(const T& t){print(t); pl();} template void printl(const Head& head, const Tail&... tail) {print(head); cout << " "; printl(tail...);} template void fin(const T& t) {printl(t); exit(0);} void Yes(bool a) {cout << (a ? "Yes" : "No") << '\n';} template void Out2(bool a, T yes, U no) {if(a) printl(yes); else printl(no);} //functions int ctoi(char c) {return c - '0';} char to_char(int x) {return x + '0';} template constexpr auto Emin(T... a) {return min(initializer_list>{a...});} template constexpr auto Emax(T... a) {return max(initializer_list>{a...});} template bool chmax(T &a, const U &b) {if (a < b) { a = b; return true;} return false;} template bool chmin(T &a, const U &b) {if (a > b) { a = b; return true;} return false;} template ll Epow(T x, U y) {ll ans = 1; for(int i = 0; i < y; i++) ans *= x; return ans;} template ll Eceil(T x, U y) {return (ll)ceil((ld)x / (ld)y);} template ll Efloor(T x, U y) {return (ll)floor((ld)x / (ld)y);} template bool check_bit(T tar, U bit) {return ((tar & Epow(2, bit)) != 0);} /*Math Library*/ //a ÷ bをmodで割った余り(modは素数) - O(log(mod)) ll div_mod(ll a, ll b, ll mod) {return (a * pow_mod(b, mod - 2, mod)) % mod;} //階乗 - O(n) ll factorial(ll n, ll mod) { ll ans = 1; for(ll i = n; i >= 2; i--) ans = (ans * i) % mod; return ans; }ll factorial(ll n) {return factorial(n, MOD);} //順列 - O(r) ll permutation(ll n, ll r, ll mod) { ll ans = 1; for(ll i = 0; i < r; i++) ans = (ans * (n - i)) % mod; return ans; }ll permutation(ll n, ll r) {return permutation(n, r, MOD);} //組み合わせ(modは素数) - O(min(r, n - r) + log(mod)) ll combination(ll n, ll r, ll mod) { r = min(r, n - r); if(r == 0) return 1; ll up = n; ll down = 1; for(int i = 1; i < r; i++) { up = (up * (n - i)) % mod; down = (down * (i + 1)) % mod; } return div_mod(up, down, mod); }ll combination(ll n, ll r) {return combination(n, r, MOD);} //nC0~nCrまでの列挙(modは素数) - O(rlog(mod)) vector getCombination_vec(ll n, ll r, ll mod) { vector ret(r + 1); ret[0] = 1; ll up = n; ll down = 1; ret[1] = div_mod(up, down, mod); for(int i = 1; i < r; i++) { up = (up * (n - i)) % mod; down = (down * (i + 1)) % mod; ret[i + 1] = div_mod(up, down, mod); } return ret; }vector getCombination_vec(ll n, ll r) {return getCombination_vec(n, r, MOD);} //素数判定 - O(√N) bool is_prime(ll N) { if (N == 1) return false; for (ll i = 2; i * i <= N; i++) { if (N % i == 0) return false; } return true; } //約数列挙 - O(√N) vector enum_divisors(ll N) { vector res; for (ll i = 1; i * i <= N; i++) { if (N % i == 0) { res.eb(i); if (N / i != i) res.eb(N / i); } } sort(all(res)); return res; } //素因数分解 - O(√N) vector> prime_factorize(ll N) { vector> res; for (ll a = 2; a * a <= N; a++) { if (N % a != 0) continue; ll ex = 0; while (N % a == 0) { ex++; N /= a; } res.eb(mp(a, ex)); } if (N != 1) res.eb(mp(N, 1)); return res; } //エラトステネスの篩 - O(NloglogN) vector Eratosthenes(ll N) { vector isprime(N + 1, true); isprime[0] = isprime[1] = false; for (ll p = 2; p <= N; p++) { if (!isprime[p]) continue; for (ll q = p * 2; q <= N; q += p) { isprime[q] = false; } } return isprime; } //N以下の素数を列挙 - O(NloglogN) vector getPrimes(ll N) { vector era = Eratosthenes(N); vector primes; for(ll i = 2; i <= N; i++) { if(era[i]) primes.eb(i); } return primes; } //--------------------------------------------------------------------------------------------------- int main() { ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(10); ll N, P; cin >> N >> P; vector prime_cnt((N + 1) * 100, 0); rep1(i, 2, N) { auto ret = prime_factorize(i); rep(j, ret.size()) prime_cnt[ret[j].fi] += ret[j].se; } ll div_cnt = prime_cnt[P]; ll Nfac = factorial(N, MODM); ll r = pow_mod(Nfac, Nfac, MODM); Mint ans = div_cnt * r; printl(ans.val()); }