結果
問題 | No.2975 単調増加部分積 |
ユーザー |
![]() |
提出日時 | 2024-11-29 21:42:15 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 27 ms / 10,000 ms |
コード長 | 32,053 bytes |
コンパイル時間 | 4,465 ms |
コンパイル使用メモリ | 283,152 KB |
実行使用メモリ | 5,248 KB |
最終ジャッジ日時 | 2024-11-29 21:42:21 |
合計ジャッジ時間 | 5,262 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
other | AC * 24 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"using namespace std;#include<bits/stdc++.h>#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"namespace noya2 {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p){os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p){is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v){int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v){for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &...u){cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &...u){cout << t;if (sizeof...(u)) cout << sep;out(u...);}template<typename T>void out(const vector<vector<T>> &vv){int s = (int)vv.size();for (int i = 0; i < s; i++) out(vv[i]);}struct IoSetup {IoSetup(){cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetup_noya2;} // namespace noya2#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"namespace noya2{const int iinf = 1'000'000'007;const long long linf = 2'000'000'000'000'000'000LL;const long long mod998 = 998244353;const long long mod107 = 1000000007;const long double pi = 3.14159265358979323;const vector<int> dx = {0,1,0,-1,1,1,-1,-1};const vector<int> dy = {1,0,-1,0,1,-1,-1,1};const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";const string alp = "abcdefghijklmnopqrstuvwxyz";const string NUM = "0123456789";void yes(){ cout << "Yes\n"; }void no(){ cout << "No\n"; }void YES(){ cout << "YES\n"; }void NO(){ cout << "NO\n"; }void yn(bool t){ t ? yes() : no(); }void YN(bool t){ t ? YES() : NO(); }} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"namespace noya2{unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){if (a == 0 || b == 0) return a + b;int n = __builtin_ctzll(a); a >>= n;int m = __builtin_ctzll(b); b >>= m;while (a != b) {int mm = __builtin_ctzll(a - b);bool f = a > b;unsigned long long c = f ? a : b;b = f ? b : a;a = (c - b) >> mm;}return a << std::min(n, m);}template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }long long sqrt_fast(long long n) {if (n <= 0) return 0;long long x = sqrt(n);while ((x + 1) * (x + 1) <= n) x++;while (x * x > n) x--;return x;}template<typename T> T floor_div(const T n, const T d) {assert(d != 0);return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);}template<typename T> T ceil_div(const T n, const T d) {assert(d != 0);return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);}template<typename T> void uniq(std::vector<T> &v){std::sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }} // namespace noya2#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"#define rep(i,n) for (int i = 0; i < (int)(n); i++)#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)#define all(v) (v).begin(),(v).end()using ll = long long;using ld = long double;using uint = unsigned int;using ull = unsigned long long;using pii = pair<int,int>;using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;namespace noya2{/* ~ (. _________ . /) */}using namespace noya2;#line 2 "c.cpp"#line 2 "/Users/noya2/Desktop/Noya2_library/fps/fps_modint.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/fps/formal_power_series.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/fps/formal_power_series.hpp"namespace noya2{template<typename T>concept Field = requires (T a, T b){a + b; a - b; a / b; a * b;T(0); T(1);};template<class Info>concept Fps_Info = requires {typename Info::value_type;requires Field<typename Info::value_type>;{Info::multiply(declval<vector<typename Info::value_type>>(),declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typenameInfo::value_type>>;{Info::inv(declval<vector<typename Info::value_type>>(),declval<int>())} -> convertible_to<vector<typename Info::value_type>>;{Info::integral(declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;};template<Fps_Info Info>struct FormalPowerSeries : vector<typename Info::value_type> {using T = typename Info::value_type;using vector<T>::vector;using vector<T>::operator=;using FPS = FormalPowerSeries;FormalPowerSeries (const vector<T> &init_ = {}){ (*this) = init_; }void shrink(){ while (!(*this).empty() && (*this).back() == T(0)) (*this).pop_back(); }FPS &operator+=(const T &r){if ((*this).empty()) (*this).resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const T &r){if ((*this).empty()) (*this).resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const T &r){for (auto &x : *this) x *= r;return *this;}FPS &operator/=(const T &r){(*this) *= T(1)/r;return *this;}FPS &operator<<=(const int &d){(*this).insert((*this).begin(),d,T(0));return *this;}FPS &operator>>=(const int &d){if ((int)(*this).size() <= d) (*this).clear();else (*this).erase((*this).begin(),(*this).begin()+d);return *this;}FPS &operator+=(const FPS &r){if ((*this).size() < r.size()) (*this).resize(r.size());for (int i = 0; i < (int)(r.size()); i++) (*this)[i] += r[i];return *this;}FPS &operator-=(const FPS &r){if ((*this).size() < r.size()) (*this).resize(r.size());for (int i = 0; i < (int)(r.size()); i++) (*this)[i] -= r[i];return *this;}FPS &operator*=(const FPS &r){if ((*this).empty() || r.empty()){(*this).clear();return *this;}(*this) = Info::multiply(*this,r);return *this;}FPS operator+(const T &r) const { return FPS(*this) += r; }FPS operator-(const T &r) const { return FPS(*this) -= r; }FPS operator*(const T &r) const { return FPS(*this) *= r; }FPS operator/(const T &r) const { return FPS(*this) /= r; }FPS operator<<(const int &d) const { return FPS(*this) <<= d; }FPS operator>>(const int &d) const { return FPS(*this) >>= d; }FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator+() const { return *this; }FPS operator-() const {FPS res(*this);for (auto &x : res) x = -x;return res;}T eval(const T &x) const {T res = T(0), w = T(1);for (auto &e : *this) res += e * w, w *= x;return res;}static FPS dot(const FPS &lhs, const FPS &rhs){FPS res(min(lhs.size(),rhs.size()));for (int i = 0; i < (int)res.size(); i++) res[i] = lhs[i] * rhs[i];return res;}FPS pre(int siz) const {FPS ret((*this).begin(), (*this).begin() + min((int)this->size(), siz));if ((int)ret.size() < siz) ret.resize(siz);return ret;}FPS rev() const {FPS ret(*this);reverse(ret.begin(), ret.end());return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));T one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {FPS ret = Info::integral(*this);return ret;}FPS inv(int d = -1) const {FPS ret = Info::inv(*this,d);return ret;}FPS exp(int d = -1) const {const int n = (*this).size();if (d == -1) d = n;FPS f = {T(1)+(*this)[0],(*this)[1]}, res = {1,(n > 1 ? (*this)[1] : 0)};for (int sz = 2; sz < d; sz <<= 1){f.insert(f.end(),(*this).begin()+min(n,sz),(*this).begin()+min(n,sz*2));if ((int)f.size() < sz*2) f.resize(sz*2);res = res * (f - res.log(2*sz));res.resize(sz*2);}res.resize(d);return res;}FPS log(int d = -1) const {assert(!(*this).empty() && (*this)[0] == T(1));if (d == -1) d = (*this).size();return (this->diff() * this->inv(d)).pre(d - 1).integral();}};} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/fps/ntt.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"namespace noya2 {constexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}constexpr bool is_prime_constexpr(int n) {if (n <= 1) return false;if (n == 2 || n == 7 || n == 61) return true;if (n % 2 == 0) return false;long long d = n - 1;while (d % 2 == 0) d /= 2;constexpr long long bases[3] = {2, 7, 61};for (long long a : bases) {long long t = d;long long y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};long long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u;auto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);// constexpr long long primitive_root_constexpr(long long m){// if (m == (1LL << 47) - (1LL << 24) + 1) return 3;// return primitive_root_constexpr(static_cast<int>(m));// }} // namespace noya2#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"namespace noya2{struct barrett {unsigned int _m;unsigned long long im;explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);unsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};template <int m>struct static_modint {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}constexpr static_modint() : _v(0) {}template<std::signed_integral T>constexpr static_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>constexpr static_modint(T v){_v = (unsigned int)(v % umod());}constexpr unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}constexpr mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}constexpr mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}constexpr mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (uint)(z % umod());return *this;}constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }constexpr mint operator+() const { return *this; }constexpr mint operator-() const { return mint() - *this; }constexpr mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}constexpr mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend constexpr mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend constexpr mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend constexpr mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend constexpr mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend constexpr bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = is_prime_flag<m>;};template <int id> struct dynamic_modint {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template<std::signed_integral T>dynamic_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>dynamic_modint(T v){_v = (unsigned int)(v % umod());}uint val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = noya2::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;template<typename T>concept Modint = requires (T &a){T::mod();a.inv();a.val();a.pow(declval<int>());};} // namespace noya2#line 5 "/Users/noya2/Desktop/Noya2_library/fps/ntt.hpp"namespace noya2{template<Modint mint>struct NTT {static constexpr uint mod = mint::mod();static constexpr ull mod2 = (ull)mod * mod;static constexpr uint pr = primitive_root_constexpr(mod);static constexpr int level = countr_zero(mod-1);mint wp[level+1], wm[level+1];void set_ws(){mint r = mint(pr).pow((mod-1) >> level);wp[level] = r, wm[level] = r.inv();for (int i = level-1; i >= 0; i--){wp[i] = wp[i+1] * wp[i+1];wm[i] = wm[i+1] * wm[i+1];}}NTT () { set_ws(); }void fft4(vector<mint> &a, int k, int s = 0){uint im = wm[2].val();uint n = 1<<k;uint len = n;int l = k;while (len > 1){if (l == 1){for (int i = 0; i < (1<<(k-1)); i++){int i0 = s + i*2, i1 = i0+1;a[i0] += a[i1];a[i1] = a[i0] - a[i1] * 2;}len >>= 1;l -= 1;}else {int len4 = len/4;int nlen = n/len;ull r1 = 1, r2 = 1, r3 = 1, imr1 = im, imr3 = im;for (int i = 0; i < len4; i++){int offset = 0;for (int j = 0; j < nlen; j++){int i0 = s + i + offset, i1 = i0 + len4, i2 = i1 + len4, i3 = i2 + len4;uint a0 = a[i0].val();uint a1 = a[i1].val();uint a2 = a[i2].val();uint a3 = a[i3].val();uint a0p2 = a0 + a2;uint a1p3 = a1 + a3;ull b0m2 = (a0 + mod - a2) * r1;ull b1m3 = (a1 + mod - a3) * imr1;ull c0m2 = (a0 + mod - a2) * r3;ull c1m3 = (a1 + mod - a3) * imr3;a[i0] = a0p2 + a1p3;a[i1] = b0m2 + b1m3;a[i2] = (a0p2 + mod*2 - a1p3) * r2;a[i3] = c0m2 + mod2*2 - c1m3;offset += len;}r1 = r1 * wm[l].val() % mod;r2 = r1 * r1 % mod;r3 = r1 * r2 % mod;imr1 = im * r1 % mod;imr3 = im * r3 % mod;}len >>= 2;l -= 2;}}}void ifft4(vector<mint> &a, int k, int s = 0){uint im = wp[2].val();uint n = 1<<k;uint len = (k & 1 ? 2 : 4);int l = (k & 1 ? 1 : 2);while (len <= n){if (l == 1){for (int i = 0; i < (1<<(k-1)); i++){int i0 = s + i*2, i1 = i0+1;a[i0] += a[i1];a[i1] = a[i0] - a[i1] * 2;}len <<= 2;l += 2;}else {int len4 = len/4;int nlen = n/len;ull r1 = 1, r2 = 1, r3 = 1, imr1 = im, imr3 = im;for (int i = 0; i < len4; i++){int offset = 0;for (int j = 0; j < nlen; j++){int i0 = s + i + offset, i1 = i0 + len4, i2 = i1 + len4, i3 = i2 + len4;ull a0 = a[i0].val();ull a1 = a[i1].val() * r1;ull a2 = a[i2].val() * r2;ull a3 = a[i3].val() * r3;ull b1 = a[i1].val() * imr1;ull b3 = a[i3].val() * imr3;ull a0p2 = a0 + a2;ull a1p3 = a1 + a3;ull a0m2 = a0 + mod2 - a2;ull b1m3 = b1 + mod2 - b3;a[i0] = a0p2 + a1p3;a[i1] = a0m2 + b1m3;a[i2] = a0p2 + mod2*2 - a1p3;a[i3] = a0m2 + mod2*2 - b1m3;offset += len;}r1 = r1 * wp[l].val() % mod;r2 = r1 * r1 % mod;r3 = r1 * r2 % mod;imr1 = im * r1 % mod;imr3 = im * r3 % mod;}len <<= 2;l += 2;}}}void ntt(vector<mint> &a) {if ((int)a.size() <= 1) return;assert(has_single_bit(a.size()));fft4(a, countr_zero(a.size()));}void intt(vector<mint> &a, bool stop = false) {if ((int)a.size() <= 1) return;assert(has_single_bit(a.size()));ifft4(a, countr_zero(a.size()));if (stop) return ;mint iv = mint(a.size()).inv();for (auto &x : a) x *= iv;}vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40){vector<mint> s(l);for (int i = 0; i < (int)a.size(); i++) for (int j = 0; j < (int)b.size(); j++) s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l) M <<= 1, ++k;set_ws();vector<mint> s(M);for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];fft4(s, k);if (a.size() == b.size() && a == b) {for (int i = 0; i < M; ++i) s[i] *= s[i];}else {vector<mint> t(M);for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];fft4(t, k);for (int i = 0; i < M; ++i) s[i] *= t[i];}ifft4(s, k);s.resize(l);mint invm = mint(M).inv();for (int i = 0; i < l; ++i) s[i] *= invm;return s;}};} // namespace noya2#line 5 "/Users/noya2/Desktop/Noya2_library/fps/fps_modint.hpp"namespace noya2{namespace ArbitraryModConvolution {constexpr int m0 = 167772161;constexpr int m1 = 469762049;constexpr int m2 = 754974721;using mint0 = static_modint<m0>;using mint1 = static_modint<m1>;using mint2 = static_modint<m2>;constexpr int r01 = mint1(m0).inv().val();constexpr int r02 = mint2(m0).inv().val();constexpr int r12 = mint2(m1).inv().val();constexpr int r02r12 = (long long)(r02) * r12 % m2;constexpr long long w1 = m0;constexpr long long w2 = (long long)(m0) * m1;template <typename T, typename submint>vector<submint> mul(const vector<T> &a, const vector<T> &b) {static NTT<submint> ntt;vector<submint> s(a.size()), t(b.size());for (int i = 0; i < (int)a.size(); ++i) s[i] = (long long)(a[i] % submint::mod());for (int i = 0; i < (int)b.size(); ++i) t[i] = (long long)(b[i] % submint::mod());return ntt.multiply(s, t);}template <typename T>vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) {auto d0 = mul<T, mint0>(s, t);auto d1 = mul<T, mint1>(s, t);auto d2 = mul<T, mint2>(s, t);int n = d0.size();vector<int> ret(n);const int W1 = w1 % mod;const int W2 = w2 % mod;for (int i = 0; i < n; i++) {int n1 = d1[i].val(), n2 = d2[i].val(), a = d0[i].val();int b = (long long)(n1 + m1 - a) * r01 % m1;int c = ((long long)(n2 + m2 - a) * r02r12 + (long long)(m2 - b) * r12) % m2;ret[i] = ((long long)(a) + (long long)(b) * W1 + (long long)(c) * W2) % mod;}return ret;}template <typename mint>vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {if (a.size() == 0 && b.size() == 0) return {};if (min<int>(a.size(), b.size()) < 128) {vector<mint> ret(a.size() + b.size() - 1);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j];return ret;}vector<int> s(a.size()), t(b.size());for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].val();for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].val();vector<int> u = multiply<int>(s, t, mint::mod());vector<mint> ret(u.size());for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]);return ret;}} // namespace ArbitraryModConvolutiontemplate<Modint T>struct fps_modint{using value_type = T;static vector<T> multiply(const vector<T> &a, const vector<T> &b){return ArbitraryModConvolution::multiply(a,b);}static vector<T> inv(const vector<T> &a, int d = -1){/*FPS inv(int d = -1) const {int n = 1;if (d < 0) d = deg();FPS g(n);g[0] = (*this)[0].inv();while (n < d) {n <<= 1;g = (g * 2 - g * g * this->pre(n)).pre(n);}g.resize(d);return g;}*/int n = 1;if (d == -1) d = a.size();vector<T> g(n);g[0] = a[0].inv();while (n < d){n <<= 1;vector<T> h(n);for (int i = 0; i < n/2; i++){h[i] = g[i] * 2;}g = multiply(g, g);g.resize(n);g = multiply(g, vector<T>(a.begin(),a.begin()+min<int>(n,a.size())));g.resize(n);for (int i = 0; i < n; i++){h[i] -= g[i];}swap(g,h);}g.resize(d);return g;}static vector<T> integral(const vector<T> &a){ assert(false); }};template<typename T> using FPS_modint = FormalPowerSeries<fps_modint<T>>;} // namespace noya2#line 4 "c.cpp"using mint = modint;using fps = FPS_modint<mint>;#line 2 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"namespace noya2 {template<typename mint>struct binomial {binomial(int len = 300000){ extend(len); }static mint fact(int n){if (n < 0) return 0;while (n >= (int)_fact.size()) extend();return _fact[n];}static mint ifact(int n){if (n < 0) return 0;while (n >= (int)_fact.size()) extend();return _ifact[n];}static mint inv(int n){return ifact(n) * fact(n-1);}static mint C(int n, int r){if (!(0 <= r && r <= n)) return 0;return fact(n) * ifact(r) * ifact(n-r);}static mint P(int n, int r){if (!(0 <= r && r <= n)) return 0;return fact(n) * ifact(n-r);}inline mint operator()(int n, int r) { return C(n, r); }template<class... Cnts>static mint M(const Cnts&... cnts){return multinomial(0,1,cnts...);}static void initialize(int len = 2){_fact.clear();_ifact.clear();extend(len);}private:static mint multinomial(const int& sum, const mint& div_prod){if (sum < 0) return 0;return fact(sum) * div_prod;}template<class... Tail>static mint multinomial(const int& sum, const mint& div_prod, const int& n1, const Tail&... tail){if (n1 < 0) return 0;return multinomial(sum+n1,div_prod*ifact(n1),tail...);}static inline std::vector<mint> _fact, _ifact;static void extend(int len = -1){if (_fact.empty()){_fact = _ifact = {1,1};}int siz = _fact.size();if (len == -1) len = siz * 2;len = (int)min<long long>(len, mint::mod() - 1);if (len < siz) return ;_fact.resize(len+1), _ifact.resize(len+1);for (int i = siz; i <= len; i++) _fact[i] = _fact[i-1] * i;_ifact[len] = _fact[len].inv();for (int i = len; i > siz; i--) _ifact[i-1] = _ifact[i] * i;}};} // namespace noya2#line 7 "c.cpp"void solve(){int n, m, p; in(n,m,p);mint::set_mod(p);auto dfs = [&](auto sfs, int l, int r) -> fps {if (r - l == 1){return fps{1, l+1};}int md = (l + r) / 2;return sfs(sfs,l,md) * sfs(sfs,md,r);};fps f = dfs(dfs,0,n);// out(f);binomial<mint> bnm(1);bnm.initialize(n);mint ans = 0;for (int s = 1; s <= m; s++){ans += f[s] * bnm.P(n-s,m-s) * bnm(m,s);}ans /= bnm.P(n,m);out(ans);}int main(){int t = 1; //in(t);while (t--) { solve(); }}