結果
問題 | No.1889 K Consecutive Ks (Hard) |
ユーザー |
![]() |
提出日時 | 2023-06-06 09:16:27 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 71 ms / 6,000 ms |
コード長 | 36,676 bytes |
コンパイル時間 | 3,961 ms |
コンパイル使用メモリ | 243,652 KB |
最終ジャッジ日時 | 2025-02-13 23:02:03 |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 22 |
ソースコード
#include <bits/stdc++.h>using namespace std;using ll = long long;using ld = long double;using pll = pair<ll, ll>;using tlll = tuple<ll, ll, ll>;constexpr ll INF = 1LL << 60;template<class T> bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return false;}template<class T> bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return false;}ll safemod(ll A, ll M) {ll res = A % M; if (res < 0) res += M; return res;}ll divfloor(ll A, ll B) {if (B < 0) A = -A, B = -B; return (A - safemod(A, B)) / B;}ll divceil(ll A, ll B) {if (B < 0) A = -A, B = -B; return divfloor(A + B - 1, B);}ll pow_ll(ll A, ll B) {if (A == 0 || A == 1) {return A;} if (A == -1) {return B & 1 ? -1 : 1;} ll res = 1; for (int i = 0; i < B; i++) {res *= A;}return res;}ll mul_limited(ll A, ll B, ll M = INF) { return B == 0 ? 0 : A > M / B ? M : A * B; }ll pow_limited(ll A, ll B, ll M = INF) { if (A == 0 || A == 1) {return A;} ll res = 1; for (int i = 0; i < B; i++) {if (res > M / A) return M; res*= A;} return res;}ll logfloor(ll A, ll B) {assert(A >= 2); ll res = 0; for (ll tmp = 1; tmp <= B / A; tmp *= A) {res++;} return res;}ll logceil(ll A, ll B) {assert(A >= 2); ll res = 0; for (ll tmp = 1; tmp < B; tmp *= A) {res++;} return res;}ll arisum_ll(ll a, ll d, ll n) { return n * a + (n & 1 ? ((n - 1) >> 1) * n : (n >> 1) * (n - 1)) * d; }ll arisum2_ll(ll a, ll l, ll n) { return n & 1 ? ((a + l) >> 1) * n : (n >> 1) * (a + l); }ll arisum3_ll(ll a, ll l, ll d) { assert((l - a) % d == 0); return arisum2_ll(a, l, (l - a) / d + 1); }template<class T> void unique(vector<T> &V) {V.erase(unique(V.begin(), V.end()), V.end());}template<class T> void sortunique(vector<T> &V) {sort(V.begin(), V.end()); V.erase(unique(V.begin(), V.end()), V.end());}#define FINALANS(A) do {cout << (A) << '\n'; exit(0);} while (false)template<class T> void printvec(const vector<T> &V) {int _n = V.size(); for (int i = 0; i < _n; i++) cout << V[i] << (i == _n - 1 ? "" : " ");cout<< '\n';}template<class T> void printvect(const vector<T> &V) {for (auto v : V) cout << v << '\n';}template<class T> void printvec2(const vector<vector<T>> &V) {for (auto &v : V) printvec(v);}//*#include <atcoder/modint>#include <atcoder/math>#include <atcoder/convolution>#include <atcoder/internal_math>using namespace atcoder;//*/template<const int MOD = 1000000007, class T>vector<T> convolution_anymod(const vector<T> &A, const vector<T> &B){int N = A.size(), M = B.size();if (min(N, M) <= 300){using mint = static_modint<MOD>;vector<mint> A2(N), B2(M);for (int i = 0; i < N; i++)A2[i] = A[i];for (int j = 0; j < M; j++)B2[j] = B[j];vector<mint> C2(N + M - 1, 0);for (int i = 0; i < N; i++)for (int j = 0; j < M; j++)C2[i + j] += A2[i] * B2[j];vector<T> C(N + M - 1);for (int i = 0; i < N + M - 1; i++)C[i] = C2[i].val();return C;}constexpr ll MOD1 = 167772161, MOD2 = 469762049, MOD3 = 1224736769;using mint2 = static_modint<MOD2>;using mint3 = static_modint<MOD3>;using mint4 = static_modint<MOD>;constexpr int i1_2 = internal::inv_gcd(MOD1, MOD2).second;constexpr int i12_3 = internal::inv_gcd(MOD1 * MOD2, MOD3).second;constexpr int m12_4 = MOD1 * MOD2 % MOD;auto C1 = convolution<MOD1>(A, B);auto C2 = convolution<MOD2>(A, B);auto C3 = convolution<MOD3>(A, B);vector<T> C(N + M - 1);for (ll i = 0; i < N + M - 1; i++){int c1 = C1[i], c2 = C2[i], c3 = C3[i];int t1 = (mint2(c2 - c1) * mint2::raw(i1_2)).val();mint3 x2_m3 = mint3::raw(c1) + mint3::raw(t1) * mint3::raw(MOD1);mint4 x2_m = mint4::raw(c1) + mint4::raw(t1) * mint4::raw(MOD1);int t2 = ((mint3::raw(c3) - x2_m3) * mint3::raw(i12_3)).val();C[i] = (x2_m + mint4::raw(t2) * mint4::raw(m12_4)).val();}return C;}template<class T>vector<T> convolution_anymod(const vector<T> &A, const vector<T> &B, const int MOD){int N = A.size(), M = B.size();if (min(N, M) <= 300){using mint = dynamic_modint<100>;mint::set_mod(MOD);vector<mint> A2(N), B2(M);for (int i = 0; i < N; i++)A2[i] = A[i];for (int j = 0; j < M; j++)B2[j] = B[j];vector<mint> C2(N + M - 1, 0);for (int i = 0; i < N; i++)for (int j = 0; j < M; j++)C2[i + j] += A2[i] * B2[j];vector<T> C(N + M - 1);for (int i = 0; i < N + M - 1; i++)C[i] = C2[i].val();return C;}constexpr ll MOD1 = 167772161, MOD2 = 469762049, MOD3 = 1224736769;using mint2 = static_modint<MOD2>;using mint3 = static_modint<MOD3>;using mint4 = dynamic_modint<100>;mint4::set_mod(MOD);constexpr int i1_2 = internal::inv_gcd(MOD1, MOD2).second;constexpr int i12_3 = internal::inv_gcd(MOD1 * MOD2, MOD3).second;auto C1 = convolution<MOD1>(A, B);auto C2 = convolution<MOD2>(A, B);auto C3 = convolution<MOD3>(A, B);vector<T> C(N + M - 1);for (ll i = 0; i < N + M - 1; i++){int c1 = C1[i], c2 = C2[i], c3 = C3[i];int t1 = (mint2(c2 - c1) * mint2::raw(i1_2)).val();mint3 x2_m3 = mint3::raw(c1) + mint3::raw(t1) * mint3::raw(MOD1);mint4 x2_m = mint4::raw(c1) + mint4::raw(t1) * mint4::raw(MOD1);int t2 = ((mint3::raw(c3) - x2_m3) * mint3::raw(i12_3)).val();C[i] = (x2_m + mint4::raw(t2) * mint4::raw(MOD1) * mint4::raw(MOD2)).val();}return C;}template<const int MOD>vector<static_modint<MOD>> convolution_anymod(const vector<static_modint<MOD>> &A, const vector<static_modint<MOD>> &B){int N = A.size(), M = B.size();vector<int> A2(N), B2(M);for (int i = 0; i < N; i++)A2[i] = A[i].val();for (int i = 0; i < M; i++)B2[i] = B[i].val();vector<int> C2 = convolution_anymod<MOD>(A2, B2);vector<static_modint<MOD>> C(N + M - 1);for (int i = 0; i < N + M - 1; i++)C[i] = static_modint<MOD>::raw(C2[i]);return C;}template<const int id>vector<dynamic_modint<id>> convolution_anymod(const vector<dynamic_modint<id>> &A, const vector<dynamic_modint<id>> &B){int N = A.size(), M = B.size();vector<int> A2(N), B2(M);for (int i = 0; i < N; i++)A2[i] = A[i].val();for (int i = 0; i < M; i++)B2[i] = B[i].val();vector<int> C2 = convolution_anymod(A2, B2, dynamic_modint<id>::mod());vector<dynamic_modint<id>> C(N + M - 1);for (int i = 0; i < N + M - 1; i++)C[i] = dynamic_modint<id>::raw(C2[i]);return C;}// https://opt-cp.com/fps-implementation/// https://qiita.com/hotman78/items/f0e6d2265badd84d429a// https://opt-cp.com/fps-fast-algorithms/// https://maspypy.com/%E5%A4%9A%E9%A0%85%E5%BC%8F%E3%83%BB%E5%BD%A2%E5%BC%8F%E7%9A%84%E3%81%B9%E3%81%8D%E7%B4%9A%E6%95%B0-%E9%AB%98%E9%80%9F%E3%81%AB%E8%A8%88%E7%AE%97%E3%81%A7%E3%81%8D%E3%82%8B%E3%82%82%E3%81%AEtemplate<class T, bool is_ntt_friendly>struct FormalPowerSeries : vector<T>{using vector<T>::vector;using vector<T>::operator=;using F = FormalPowerSeries;using S = vector<pair<ll, T>>;FormalPowerSeries(const S &f, int n = -1){if (n == -1)n = f.back().first + 1;(*this).assign(n, T(0));for (auto [d, a] : f)(*this)[d] += a;}F operator-() const{F res(*this);for (auto &a : res)a = -a;return res;}F operator*=(const T &k){for (auto &a : *this)a *= k;return *this;}F operator*(const T &k) const { return F(*this) *= k; }friend F operator*(const T k, const F &f) { return f * k; }F operator/=(const T &k){*this *= k.inv();return *this;}F operator/(const T &k) const { return F(*this) /= k; }F &operator+=(const F &g){int n = (*this).size(), m = g.size();(*this).resize(max(n, m), T(0));for (int i = 0; i < m; i++)(*this)[i] += g[i];return *this;}F operator+(const F &g) const { return F(*this) += g; }F &operator-=(const F &g){int n = (*this).size(), m = g.size();(*this).resize(max(n, m), T(0));for (int i = 0; i < m; i++)(*this)[i] -= g[i];return *this;}F operator-(const F &g) const { return F(*this) -= g; }F &operator<<=(const ll d){int n = (*this).size();(*this).insert((*this).begin(), min(ll(n), d), T(0));(*this).resize(n);return *this;}F operator<<(const ll d) const { return F(*this) <<= d; }F &operator>>=(const ll d){int n = (*this).size();(*this).erase((*this).begin(), (*this).begin() + min(ll(n), d));(*this).resize(n, T(0));return *this;}F operator>>(const ll d) const { return F(*this) >>= d; }F &operator*=(const S &g){int n = (*this).size();auto [d, c] = g.front();if (d != 0)c = 0;for (int i = n - 1; i >= 0; i--){(*this)[i] *= c;for (auto &[j, b] : g){if (j == 0)continue;if (j > i)break;(*this)[i] += (*this)[i - j] * b;}}return *this;}F operator*(const S &g) const { return F(*this) *= g; }F &operator/=(const S &g){int n = (*this).size();auto [d, c] = g.front();assert(d == 0 && c != T(0));T inv_c = c.inv();for (int i = 0; i < n; i++){for (auto &[j, b] : g){if (j == 0)continue;if (j > i)break;(*this)[i] -= (*this)[i - j] * b;}(*this)[i] *= inv_c;}return *this;}F operator/(const S &g) const { return F(*this) /= g; }// (1 + cx^d) を掛けるF multiply(const int d, const T c){int n = (*this).size();if (c == T(1)){for (int i = n - 1 - d; i >= 0; i--)(*this)[i + d] += (*this)[i];}else if (c == T(-1)){for (int i = n - 1 - d; i >= 0; i--)(*this)[i + d] -= (*this)[i];}else{for (int i = n - 1 - d; i >= 0; i--)(*this)[i + d] += (*this)[i] * c;}return *this;}F multiplication(const int d, const T c) const { return multiply(F(*this)); }// (1 + cx^d) で割るF divide(const int d, const T c){int n = (*this).size();if (c == T(1)){for (int i = 0; i < n - d; i++)(*this)[i + d] -= (*this)[i];}else if (c == T(-1)){for (int i = 0; i < n - d; i++)(*this)[i + d] += (*this)[i];}else{for (int i = 0; i < n - d; i++)(*this)[i + d] -= (*this)[i] * c;}return *this;}F division(const int d, const T c) const { return divide(F(*this)); }template<const int MOD>F convolution2(const vector<static_modint<MOD>> &A, const vector<static_modint<MOD>> &B, const int d = -1) const{F res;if (is_ntt_friendly)res = convolution(A, B);elseres = convolution_anymod(A, B);if (d != -1 && (int)res.size() > d)res.resize(d);return res;}template<const int id>F convolution2(const vector<dynamic_modint<id>> &A, const vector<dynamic_modint<id>> &B, const int d = -1) const{F res;res = convolution_anymod(A, B);if (d != -1 && (int)res.size() > d)res.resize(d);return res;}F &operator*=(const F &g){int n = (*this).size();if (n == 0)return *this;*this = convolution2(*this, g, n);return *this;}F operator*(const F &g) const { return F(*this) *= g; }template <const int MOD>void butterfly2(FormalPowerSeries<static_modint<MOD>, true> &A) const { internal::butterfly(A); }template <const int MOD>void butterfly2(FormalPowerSeries<static_modint<MOD>, false> &A) const { assert(false); }template <const int id>void butterfly2(FormalPowerSeries<dynamic_modint<id>, false> &A) const { assert(false); }template <const int MOD>void butterfly_inv2(FormalPowerSeries<static_modint<MOD>, true> &A) const { internal::butterfly_inv(A); }template <const int MOD>void butterfly_inv2(FormalPowerSeries<static_modint<MOD>, false> &A) const { assert(false); }template <const int id>void butterfly_inv2(FormalPowerSeries<dynamic_modint<id>, false> &A) const { assert(false); }// mod (x^n - 1) をとったものを返すF circular_mod(int n) const{F res(n, T(0));for (int i = 0; i < (*this).size(); i++)res[i % n] += (*this)[i];return res;}F inv(int d = -1) const{int n = (*this).size();assert(n != 0 && (*this).front() != 0);if (d == -1)d = n;assert(d > 0);F f, g2;F g{(*this).front().inv()};while ((int)g.size() < d){if (is_ntt_friendly){int m = g.size();f = F{(*this).begin(), (*this).begin() + min(n, 2 * m)};g2 = F(g);f.resize(2 * m, T(0)), butterfly2(f);g2.resize(2 * m, T(0)), butterfly2(g2);for (int i = 0; i < 2 * m; i++)f[i] *= g2[i];butterfly_inv2(f);f.erase(f.begin(), f.begin() + m);f.resize(2 * m, T(0)), butterfly2(f);for (int i = 0; i < 2 * m; i++)f[i] *= g2[i];butterfly_inv2(f);T iz = T(2 * m).inv();iz *= -iz;for (int i = 0; i < m; i++)f[i] *= iz;g.insert(g.end(), f.begin(), f.begin() + m);}else{g.resize(2 * g.size(), T(0));g *= F{T(2)} - g * (*this);}}return {g.begin(), g.begin() + d};}F &operator/=(const F &g){*this *= g.inv((*this).size());return *this;}F operator/(const F &g) const { return F(*this) *= g.inv((*this).size()); }F differentiate(){*this >>= 1;for (int i = 0; i < int((*this).size()) - 1; i++)(*this)[i] *= i + 1;return *this;}F differential() const { return F(*this).differentiate(); }F integrate(){int n = (*this).size();vector<T> minv(n);minv[1] = T(1);*this <<= 1;for (int i = 2; i < n; i++){minv[i] = -minv[T::mod() % i] * (T::mod() / i);(*this)[i] *= minv[i];}return *this;}F integral() const { return F(*this).integrate(); }F log() const{assert((*this).front() == T(1));return ((*this).differential() / (*this)).integral();}F exp() const // https://arxiv.org/pdf/1301.5804.pdf{int n = (*this).size();assert(n != 0 && (*this).front() == T(0));//*if (is_ntt_friendly){F f{T(1)}, g{T(1)};F dh = (*this).differential();F f2, g2, f3, q, s, h, u;g2 = {T(0)};while ((int)f.size() < n){int m = f.size();T im = T(m).inv(), i2m = T(2 * m).inv();f2 = F(f);f2.resize(2 * m), butterfly2(f2);// aF f3(f);butterfly2(f3);for (int i = 0; i < m; i++)f3[i] *= g2[i];butterfly_inv2(f3);f3.erase(f3.begin(), f3.begin() + m / 2);f3.resize(m, T(0)), butterfly2(f3);for (int i = 0; i < m; i++)f3[i] *= g2[i];butterfly_inv2(f3);for (int i = 0; i < m / 2; i++)f3[i] *= -im * im;g.insert(g.end(), f3.begin(), f3.begin() + m / 2);g2 = F(g), g2.resize(2 * m), butterfly2(g2);// b, cq = F(dh);q.resize(2 * m);for (int i = m - 1; i < 2 * m; i++)q[i] = T(0);butterfly2(q);for (int i = 0; i < 2 * m; i++)q[i] *= f2[i];butterfly_inv2(q);q = q.circular_mod(m);for (int i = 0; i < m; i++)q[i] *= i2m;// d, eq.resize(m + 1);s = ((f.differential() - q) << 1).circular_mod(m);s.resize(2 * m);butterfly2(s);for (int i = 0; i < 2 * m; i++)s[i] *= g2[i];butterfly_inv2(s);for (int i = 0; i < m; i++)s[i] *= i2m;s.resize(m);// f, gh = (*this);h.resize(2 * m), s.resize(2 * m);u = (h - (s << (m - 1)).integral()) >> m;butterfly2(u);for (int i = 0; i < 2 * m; i++)u[i] *= f2[i];butterfly_inv2(u);for (int i = 0; i < m; i++)u[i] *= i2m;u.resize(m);// hf.insert(f.end(), u.begin(), u.end());}return {f.begin(), f.begin() + n};}else//*/{F f{T(1)}, g{T(1)};while ((int)f.size() < n){int m = f.size();g = convolution2(g, F{T(2)} - f * g, m);F q = (*this).differential();q.resize(m - 1);F r = f.convolution2(f, q).circular_mod(m);r.resize(m + 1);F s = ((f.differential() - r) << 1).circular_mod(m);F t = g * s;F h = (*this);h.resize(2 * m), t.resize(2 * m);F u = (h - (t << (m - 1)).integral()) >> m;F v = f * u;f.insert(f.end(), v.begin(), v.end());}return {f.begin(), f.begin() + n};/*F f{T(1)};while ((int)f.size() < n){int m = f.size();f.resize(min(n, 2 * m), T(0));f *= (*this) + F{T(1)} - f.log();}return f;//*/}}F pow(const ll k) const{if (k == 0){F res((*this).size(), T(0));res[0] = T(1);return res;}int n = (*this).size(), d;for (d = 0; d < n; d++){if ((*this)[d] != T(0))break;}if (d == n)return F(n, 0);F res = F(*this) >> d;T c = res[0];res /= c;res = (res.log() * T(k)).exp();res *= c.pow(k), res <<= (d != 0 && k > n ? n : d * k);return res;}F powmod(ll k, const F &g) const{F res(2 * g.size(), 0);res.front() = 1;F tmp = (*this) % g;tmp.resize(g.size());while (k > 0){if (k & 1){res *= tmp;res %= g;res.resize(2 * g.size());}tmp = tmp.convolution2(tmp, tmp);tmp %= g;tmp.resize(g.size());k >>= 1;}return res;}// 素数 mod を要求// 存在しないなら空配列を返すF sqrt() const{int n = (*this).size(), d;for (d = 0; d < n; d += 2){if ((*this)[d] != 0)break;if (d + 1 < n && (*this)[d + 1] != 0)return F(0);}if (d >= n)return F(n, 0);T a = (*this)[d];int p = T::mod();if (a.pow((p - 1) / 2) == p - 1)return F(0);T r;if (p % 4 == 3)r = a.pow((p + 1) / 4);else{int q = p - 1, s = 0;while (q % 2 == 0)q /= 2, s++;T z = 2;while (z.pow((p - 1) / 2) != p - 1)z++;int m = s;T c = z.pow(q);T t = a.pow(q);r = a.pow((q + 1) / 2);while (t != 1){int m2 = 1;for (T tmp = t * t; tmp != 1; tmp = tmp * tmp, m2++);T b = c.pow(1 << (m - m2 - 1));m = m2, c = b * b, t *= c, r *= b;}}T inv_2 = T(2).inv();F f = F(*this) >> d, res = F{r};while (res.size() < f.size()){res.resize(min(f.size(), 2 * res.size()), T(0));res = (res + res.inv() * f) * inv_2;}res <<= d / 2;return res;}F div_poly(const F &g) const{int n = (*this).size(), m = g.size();int k = n - m + 1;if (k <= 0)return F{};F f2 = F(*this), g2 = F(g);reverse(f2.begin(), f2.end());reverse(g2.begin(), g2.end());f2.resize(k, T(0)), g2.resize(k, T(0));F q = f2 / g2;reverse(q.begin(), q.end());while (!q.empty() && q.back() == T(0))q.pop_back();return q;}pair<F, F> divmod(const F &g) const{int m = g.size();assert(m != 0);F q = (*this).div_poly(g);F f3 = F(*this), g3 = F(g), q3 = F(q);f3.resize(m - 1, T(0)), g3.resize(m - 1, T(0)), q3.resize(m - 1, T(0));F r = f3 - q3 * g3;while (!r.empty() && r.back() == T(0))r.pop_back();return make_pair(q, r);}F operator%(const F &g) const { return (*this).divmod(g).second; }F &operator%=(const F &g) { return (*this) = (*this) % g; }T eval(const T &x){T res(0);for (int i = (int)(*this).size() - 1; i >= 0; i--){res *= x;res += (*this)[i];}return res;}F taylor_shift(const T &c){int n = (*this).size();F fac(n), finv(n);fac[0] = 1;for (int i = 1; i < n; i++)fac[i] = fac[i - 1] * i;finv[n - 1] = fac[n - 1].inv();for (int i = n - 2; i >= 0; i--)finv[i] = finv[i + 1] * (i + 1);F f = F(*this), g = F(n);for (int i = 0; i < n; i++)f[i] *= fac[i];g[0] = 1;for (int i = 1; i < n; i++)g[i] = c * g[i - 1];for (int i = 0; i < n; i++)g[i] *= finv[i];reverse(f.begin(), f.end());F h = f * g;reverse(h.begin(), h.end());for (int i = 0; i < n; i++)h[i] *= finv[i];return h;}vector<T> eval_multipoint(const vector<T> &xs){int m0 = xs.size(), m = 1;while (m < m0)m <<= 1;vector<F> node(2 * m, F{1});for (int i = 0; i < m0; i++)node[m + i] = {-xs[i], T(1)};for (int i = m - 1; i > 0; i--)node[i] = convolution2(node[i << 1], node[(i << 1) | 1]);node[1] = (*this).divmod(node[1]).second;for (int i = 2; i < m + m0; i++)node[i] = node[i >> 1].divmod(node[i]).second;vector<T> res(m0);for (int i = 0; i < m0; i++)res[i] = node[m + i].empty() ? T(0) : node[m + i][0];return res;}};// (次数, 係数) を昇順に並べたものtemplate <class T, bool is_ntt_friendly>struct SparseFormalPowerSeries : vector<pair<ll, T>>{using vector<pair<ll, T>>::vector;using vector<pair<ll, T>>::operator=;using F = FormalPowerSeries<T, is_ntt_friendly>;using S = SparseFormalPowerSeries;F to_fps(int n) const{F res(n, T(0));for (auto [d, a] : (*this))res[d] += a;return res;}SparseFormalPowerSeries(const F &f){(*this).clear();for (int i = 0; i < (int)f.size(); i++){if (f[i] != T(0))(*this).emplace_back(make_pair(i, f[i]));}}S operator-() const{S res(*this);for (auto &[d, a] : res)a = -a;return res;}S operator*=(const T &k){for (auto &[d, a] : (*this))a *= k;return (*this);}S operator/=(const T &k){(*this) *= k.inv();return (*this);}S operator*(const T &k) const { return (*this) *= k; }S operator/(const T &k) const { return (*this) /= k; }S operator+(const S &g) const{S res;int n = (*this).size(), m = g.size(), i = 0, j = 0;while (i < n || j < m){pair<ll, T> tmp;if (j == m || (i != n && (*this)[i].first <= g[j].first))tmp = (*this)[i++];elsetmp = g[j++];if (!res.empty() && res.back().first == tmp.first)res.back().second += tmp.second;elseres.emplace_back(tmp);}return res;}S operator-(const S &g) const{S res;int n = (*this).size(), m = g.size(), i = 0, j = 0;while (i < n || j < m){pair<ll, T> tmp;if (j == m || (i != n && (*this)[i].first <= g[j].first))tmp = (*this)[i++];else{tmp = g[j++];tmp.second = -tmp.second;}if (!res.empty() && res.back().first == tmp.first)res.back().second += tmp.second;elseres.emplace_back(tmp);}return res;}S operator*(const S &g) const{S res;for (auto [d, a] : (*this))for (auto [e, b] : (*this))res.emplace_back(make_pair(d + e, a * b));sort(res.begin(), res.end());S res2;for (auto da : res){auto [d, a] = da;if (res2.empty() || res2.back() != d)res2.emplace_back(da);elseres2.back() += a;}return res;}S operator+=(const S &g) { return (*this) = (*this) + g; }S operator-=(const S &g) { return (*this) = (*this) - g; }S operator*=(const S &g) { return (*this) = (*this) * g; }S operator<<=(ll k){for (auto &[d, a] : (*this))d += k;return (*this);}S operator<<(ll k) const { return (*this) <<= k; }S operator>>(ll k) const{S res;for (auto [d, a] : (*this)){d -= k;if (d >= 0)res.emplace_back(make_pair(d, a));}return res;}S operator>>=(ll k) { return (*this) = (*this) >> k; }F inv(int n) const{F f(n, T(0));f.front() = T(1);return f / (*this);}S differentiate(){for (auto &[d, a] : (*this))a *= d--;if (!(*this).empty() && (*this).front().first == -1)(*this).erase((*this).begin());return (*this);}S differential() const { return S(*this).differentiate(); }S integrate(){for (auto &[d, a] : (*this))a /= T(++d);return (*this);}S integral() const { return S(*this).integrate(); }F log(int n) const{F f = (*this).to_fps(n);return (f.differential() / (*this)).integral();}F exp(int n) const{vector<T> minv(n);minv[1] = T(1);for (int i = 2; i < n; i++)minv[i] = -minv[T::mod() % i] * (T::mod() / i);S fd = (*this).differential();F g(n, T(0));g[0] = T(1);for (int i = 0; i < n - 1; i++){for (auto [d, a] : fd){if (i - d < 0)break;g[i + 1] += a * g[i - d];}g[i + 1] *= minv[i + 1];}return g;}// バグっていますF pow(ll m, int n) const{if (m == 0){F res(n, T(0));res.front() = T(1);return res;}if ((*this).empty())return F(n, T(0));vector<T> minv(n);minv[1] = T(1);for (int i = 2; i < n; i++)minv[i] = -minv[T::mod() % i] * (T::mod() / i);S f = (*this) >> (*this).front().first;S fd = f.differential();F g(n, T(0)), gd(n, T(0));g[0] = f.front().second.pow(m);int len = m > n ? n - 1 : min(f.back().first * m, ll(n - 1));for (int i = 0; i < len; i++){for (auto [d, a] : fd){if (i - d < 0)break;gd[i] += a * g[i - d];}gd[i] *= m;for (auto [d, a] : f){if (d == 0)continue;if (i - d < 0)break;gd[i] -= a * gd[i - d];}g[i + 1] = gd[i] * minv[i + 1];}return g << ((*this).front().first != 0 && m > n ? n : (*this).front().first * m);}};template<class T, bool is_ntt_friendly>struct RationalFormalPowerSeries{using F = FormalPowerSeries<T, is_ntt_friendly>;using R = RationalFormalPowerSeries;F num, den;R operator-() const{R res(*this);res.num = -res.num;return res;}R operator*=(const T &k){(*this).num *= k;return *this;}R operator*(const T &k) const { return R(*this) *= k; }friend R operator*(const T k, const R &r) { return r * k; }R operator/=(const T &k){(*this).den *= k;return k;}R operator/(const T &k) const { return R(*this) /= k; }R &operator+=(const R &r){F f, g;f = f.convolution2((*this).num, r.den);g = g.convolution2((*this).den, r.num);(*this).num = f + g;(*this).den = (*this).den.convolution2((*this).den, r.den);return *this;}R operator+(const R &r) const { return R(*this) += r; }R &operator-=(const R &r){F f, g;f = f.convolution2((*this).num, r.den);g = g.convolution2((*this).den, r.num);(*this).num = f - g;(*this).den = (*this).den.convolution2((*this).den, r.den);return *this;}R operator-(const R &r) const { return R(*this) -= r; }R operator*=(const R &r){(*this).num = (*this).num.convolution2((*this).num, r.num);(*this).den = (*this).den.convolution2((*this).den, r.den);return *this;}R operator*(const R &r) const { return R(*this) *= r; }R operator/=(const R &r){(*this).num = (*this).num.convolution2((*this).num, r.den);(*this).den = (*this).den.convolution2((*this).den, r.num);return *this;}R operator/(const R &r) const { return R(*this) /= r; }R inv(){R res(*this);swap(res.num, res.den);return res;}};template <class T, bool is_ntt_friendly>FormalPowerSeries<T, is_ntt_friendly> convolution_many(const vector<FormalPowerSeries<T, is_ntt_friendly>> &fs, int d = -1){using F = FormalPowerSeries<T, is_ntt_friendly>;if ((int)fs.size() == 0)return F{1};deque<F> deq;for (auto f : fs)deq.push_back(f);while ((int)deq.size() > 1){F f = deq.front();deq.pop_front();F g = deq.front();deq.pop_front();f = f.convolution2(f, g, d);deq.push_back(f);}if (d != -1)deq.front().resize(d);return deq.front();}template <class T, bool is_ntt_friendly>RationalFormalPowerSeries<T, is_ntt_friendly> rational_sum(const vector<RationalFormalPowerSeries<T, is_ntt_friendly>> &rs, int d = -1){using R = RationalFormalPowerSeries<T, is_ntt_friendly>;if (rs.size() == 0)return R{{1}, {1}};vector<R> res = vector<R>(rs);while (res.size() > 1){vector<R> nxt;for (int i = 0; i < (int)res.size(); i += 2){if (i + 1 < (int)res.size())nxt.emplace_back(res[i] + res[i + 1]);elsenxt.emplace_back(res[i]);if (d != -1){if ((int)nxt.back().num.size() > d)nxt.back().num.resize(d);if ((int)nxt.back().den.size() > d)nxt.back().den.resize(d);}}res = nxt;}if (d != -1)res.front().num.resize(d), res.front().den.resize(d);return res.front();}template <class T, bool is_ntt_friendly>FormalPowerSeries<T, is_ntt_friendly> interpolation(const vector<T> &xs, const vector<T> &ys){using F = FormalPowerSeries<T, is_ntt_friendly>;using R = RationalFormalPowerSeries<T, is_ntt_friendly>;int n = xs.size();assert(n == ys.size());vector<F> fs(n);for (int i = 0; i < n; i++)fs[i] = F{-xs[i], T(1)};F g = convolution_many(fs);F h = g.differential();vector<T> a = h.eval_multipoint(xs);vector<R> rs(n);for (int i = 0; i < n; i++)rs[i] = R{F{ys[i] / a[i]}, fs[i]};R q = rational_sum(rs, n);return q.num;}// prod[d in D](1 + cx^d) を M 次の項まで求めるtemplate <class T, bool is_ntt_friendly>FormalPowerSeries<T, is_ntt_friendly> multiply_many(const int &M, const T &c, const vector<int> &D){using F = FormalPowerSeries<T, is_ntt_friendly>;vector<int> cnt(M + 1, 0);for (auto d : D){if (d < 0 || M < d)continue;cnt[d]++;}vector<T> inv(M + 1);inv[1] = T(1);for (int i = 2; i <= M; i++)inv[i] = -inv[T::mod() % i] * (T::mod() / i);F f(M + 1, 0);for (int k = 1; k <= M; k++){T pw = 1;for (int i = 1; k * i <= M; i++){pw *= c;if (i & 1)f[k * i] += T::raw(cnt[k]) * pw * inv[i];elsef[k * i] -= T::raw(cnt[k]) * pw * inv[i];}}return f.exp();}// 多重集合 S の要素から何個か選んで総和を 0, 1, …, M にする方法の数template <class T, bool is_ntt_friendly>FormalPowerSeries<T, is_ntt_friendly> subset_sum(const int &M, const vector<int> &S){return multiply_many<T, is_ntt_friendly>(M, T(1), S);}// 集合 S の各要素が無限個ある集合 T から何個か選んで総和を 0, 1, …, M にする方法の数template <class T, bool is_ntt_friendly>FormalPowerSeries<T, is_ntt_friendly> partition(const int &M, const vector<int> &S){return multiply_many<T, is_ntt_friendly>(M, T(-1), S).inv();}template<class T, bool is_ntt_friendly>FormalPowerSeries<T, is_ntt_friendly> stirling1(const int &N){using F = FormalPowerSeries<T, is_ntt_friendly>;using S = vector<pair<int, T>>;if (N == 0)return {1};if (N == 1)return {0, 1};if (N & 1){F f = stirling1<T, is_ntt_friendly>(N - 1);f.resize(N + 1, T(0));return f * S{{0, 1 - N}, {1, 1}};}else{F f = stirling1<T, is_ntt_friendly>(N / 2);f.resize(N + 1, T(0));F g = f.taylor_shift(-(N / 2));return f * g;}}template<class T, bool is_ntt_friendly>FormalPowerSeries<T, is_ntt_friendly> stirling2(const int &N){using F = FormalPowerSeries<T, is_ntt_friendly>;vector<T> fac(N + 1, T(0)), finv(N + 1, T(0));fac[0] = T(1);for (int i = 1; i <= N; i++)fac[i] = fac[i - 1] * i;finv[N] = fac[N].inv();for (int i = N - 1; i >= 0; i--)finv[i] = finv[i + 1] * (i + 1);vector<int> minfactor(N + 1, -1);for (int i = 2; i <= N; i++){if (minfactor[i] != -1)continue;for (int k = 2 * i; k <= N; k += i)minfactor[k] = i;}vector<T> power(N + 1);for (int i = 0; i <= N; i++){if (minfactor[i] == -1)power[i] = T(i).pow(N);elsepower[i] = power[minfactor[i]] * power[i / minfactor[i]];}F A(N + 1), B(N + 1);for (int i = 0; i <= N; i++){A[i] = power[i] * finv[i];B[i] = (i & 1) ? -finv[i] : finv[i];}return A * B;}template<class T, bool is_ntt_friendly>FormalPowerSeries<T, is_ntt_friendly> bernoulli_number(const int &N){using F = FormalPowerSeries<T, is_ntt_friendly>;F fac(N + 2, T(0)), finv(N + 2, T(0));fac[0] = T(1);for (int i = 1; i <= N + 1; i++)fac[i] = fac[i - 1] * i;finv[N + 1] = fac[N + 1].inv();for (int i = N; i >= 0; i--)finv[i] = finv[i + 1] * (i + 1);F f = (finv >> 1).inv();for (int i = 0; i <= N; i++)f[i] *= fac[i];f.pop_back();return f;}// [x^N] P(x)/Q(x) を求める(P の次数は Q の次数より小さい)template<class T, bool is_ntt_friendly>T bostan_mori(const FormalPowerSeries<T, is_ntt_friendly> &P, const FormalPowerSeries<T, is_ntt_friendly> &Q, ll N){using F = FormalPowerSeries<T, is_ntt_friendly>;int d = (int)Q.size() - 1;assert((int)P.size() <= d);if (is_ntt_friendly){int z = 1;while (z < 2 * d + 1)z <<= 1;T iz = T(z).inv();F U = F(P), V = F(Q);U.resize(z), V.resize(z);while (N > 0){U.butterfly2(U), V.butterfly2(V);for (int i = 0; i < z; i += 2){T x = V[i + 1], y = V[i];U[i] *= x, V[i] *= x;U[i + 1] *= y, V[i + 1] *= y;}U.butterfly_inv2(U), V.butterfly_inv2(V);for (int i = 0; i < (z >> 1); i++){U[i] = U[2 * i + (N & 1)] * iz;V[i] = V[2 * i] * iz;}for (int i = (z >> 1); i < z; i++)U[i] = 0, V[i] = 0;N >>= 1;}return U.front() / V.front();}else{F U = F(P), V = F(Q);U.resize(d), V.resize(d + 1);while (N > 0){F U2 = F(U), V2 = F(V), V3 = F(V);for (int i = 1; i <= d; i += 2)V3[i] = -V3[i];U2 *= V3, V2 *= V3;for (int i = 0; i <= d; i++){U[i] = U2[2 * i + (N & 1)];V[i] = V2[2 * i];}N >>= 1;}return U.front() / V.front();}}// a_n = sum[i = 1..d] c_i a_{n-i}(n ≥ d)を満たすとき、a_N を求める(A は 0-indexed で C は 1-indexed)template<class T, bool is_ntt_friendly>T linear_recurrence(const vector<T> &A, const vector<T> &C, ll N){using F = FormalPowerSeries<T, is_ntt_friendly>;int d = C.size();assert((int)A.size() >= d);F Ga(d), Q(d + 1);Q[0] = 1;for (int i = 0; i < d; i++)Ga[i] = A[i], Q[i + 1] = -C[i];F P = Ga * Q;return bostan_mori(P, Q, N);}// https://37zigen.com/multipoint-evaluation/#i-2template<class T, bool is_ntt_friendly>T factorial_fast(ll N){using F = FormalPowerSeries<T, is_ntt_friendly>;if (N >= T::mod())return 0;int M = sqrt(N);vector<F> fs(M);for (int i = 0; i < M; i++)fs[i] = {i + 1, 1};F f = convolution_many(fs);vector<T> xs(M);for (int i = 0; i < M; i++)xs[i] = i * M;vector<T> ys = f.eval_multipoint(xs);T res = 1;for (auto y : ys)res *= y;for (int i = M * M + 1; i <= N; i++)res *= i;return res;}//*using mint = modint998244353;const bool ntt = true;//*//*using mint = modint1000000007;const bool ntt = false;//*//*using mint = modint;const bool ntt = false;//*/using fps = FormalPowerSeries<mint, ntt>;using sfps = SparseFormalPowerSeries<mint, ntt>;using rfps = RationalFormalPowerSeries<mint, ntt>;int main(){ll N, M;cin >> N >> M;fps g(N + 1, 0);for (ll i = 1; i <= M; i++){for (ll j = 0; i * j <= N; j++){if (1 + i * j <= N)g.at(1 + i * j) += 1;if (i + i * j <= N)g.at(i + i * j) -= 1;}}fps f = (fps{1} - g).inv();mint ans = mint(M).pow(N) - f.at(N);cout << ans.val() << endl;}