結果
| 問題 | No.2705 L to R Graph (Another ver.) |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2024-03-29 22:27:13 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 9,377 bytes |
| コンパイル時間 | 1,684 ms |
| コンパイル使用メモリ | 127,348 KB |
| 実行使用メモリ | 7,296 KB |
| 最終ジャッジ日時 | 2024-09-30 16:18:51 |
| 合計ジャッジ時間 | 132,229 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 6 ms
6,016 KB |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | TLE | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | WA | - |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | TLE | - |
| testcase_24 | TLE | - |
| testcase_25 | TLE | - |
| testcase_26 | TLE | - |
| testcase_27 | TLE | - |
| testcase_28 | TLE | - |
| testcase_29 | TLE | - |
| testcase_30 | TLE | - |
| testcase_31 | TLE | - |
| testcase_32 | TLE | - |
| testcase_33 | TLE | - |
| testcase_34 | TLE | - |
| testcase_35 | TLE | - |
| testcase_36 | TLE | - |
| testcase_37 | TLE | - |
| testcase_38 | TLE | - |
| testcase_39 | TLE | - |
| testcase_40 | TLE | - |
| testcase_41 | TLE | - |
| testcase_42 | TLE | - |
| testcase_43 | TLE | - |
| testcase_44 | TLE | - |
| testcase_45 | TLE | - |
| testcase_46 | TLE | - |
| testcase_47 | TLE | - |
| testcase_48 | TLE | - |
| testcase_49 | TLE | - |
| testcase_50 | TLE | - |
| testcase_51 | TLE | - |
| testcase_52 | TLE | - |
ソースコード
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")
////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
static unsigned M;
static unsigned long long NEG_INV_M;
static void setM(unsigned m) { M = m; NEG_INV_M = -1ULL / M; }
unsigned x;
ModInt() : x(0U) {}
ModInt(unsigned x_) : x(x_ % M) {}
ModInt(unsigned long long x_) : x(x_ % M) {}
ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) {
const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
const unsigned long long r = y - M * q;
x = r - M * (r >= M);
return *this;
}
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////
using Mint = ModInt;
constexpr int LIM_INV = 200'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];
void prepare() {
inv[1] = 1;
for (int i = 2; i < LIM_INV; ++i) {
inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
}
fac[0] = invFac[0] = 1;
for (int i = 1; i < LIM_INV; ++i) {
fac[i] = fac[i - 1] * i;
invFac[i] = invFac[i - 1] * inv[i];
}
}
Mint binom(Int n, Int k) {
if (n < 0) {
if (k >= 0) {
return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
} else if (n - k >= 0) {
return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
} else {
return 0;
}
} else {
if (0 <= k && k <= n) {
assert(n < LIM_INV);
return fac[n] * invFac[k] * invFac[n - k];
} else {
return 0;
}
}
}
// N^N * N(N+1)/2 * N(N-1)
// F, [L, R], S != T
Mint slow(int N) {
Mint ans = 0;
for (int L = 1; L <= N; ++L) for (int R = L; R <= N; ++R) {
vector<int> can(N + 1, 0);
for (int x = 1; L * x <= N; ++x) {
for (int d = L * x; d <= R * x && d <= N; ++d) can[d] = 1;
}
Mint here = 0;
// direct
for (int d = 1; d <= N - 1; ++d) if (can[d]) {
here += fac[N] * invFac[N - (d + 1)] * Mint(N).pow(N - d);
}
// cycle
for (int a = 0; a <= N - 1; ++a) for (int b = 0; a + b <= N - 1; ++b) for (int c = 1; a + b + c <= N; ++c) {
const int d = a + b, m = b + c;
if (d == 0) continue;
if (can[d]) continue;
if (L < R || d % __gcd(L, m) == 0) {
here += fac[N] * invFac[N - (a + b + c)] * Mint(N).pow(N - (a + b + c));
}
}
ans += here;
}
return ans;
}
Mint slow2(int N) {
vector<Mint> path(N, 0);
for (int L = 1; L <= N; ++L) for (int R = L; R <= N; ++R) {
vector<int> can(N, 0);
for (int x = 0; L * x <= N; ++x) {
for (int d = L * x; d <= min(R * x, N - 1); ++d) {
can[d] = 1;
}
}
for (int d = 0; d <= N - 1; ++d) if (can[d]) {
path[d] += 1;
}
}
cerr<<"N = "<<N<<": path = "<<path<<endl;
for (int d = 1; d <= N - 1; ++d) path[d] += path[d - 1];
Mint ans = 0;
// fix rho
for (int h = 0; h <= N - 1; ++h) for (int m = 1; h + m <= N; ++m) {
const Mint way = fac[N] * invFac[N - (h + m)] * Mint(N).pow(N - (h + m));
// before cycle
if (h) ans += way * path[h - 1];
// cycle
for (int L = 1; L <= N; ++L) ans += way * Mint(m / __gcd(L, m));
ans += way * Mint((Int)N * (N - 1) / 2) * Mint(m);
}
// S = T
ans -= Mint(N).pow(N) * Mint((Int)N * (N + 1) / 2) * N;
return ans;
}
Mint fast(int N) {
vector<Mint> path(N, 0);
// R x < d < L (x+1)
for (int d = 0; d <= N - 1; ++d) {
path[d] = Mint((Int)N * (N + 1) / 2);
if (d == 0) continue;
/*
for (int x = 0; x <= N; ++x) {
const int L = d / (x + 1) + 1;
const int R = x ? ((d + x - 1) / x - 1) : N;
if (L <= R) {
path[d] -= (Int)(R - L + 1) * (R - L + 2) / 2;
}
}
*/
vector<int> xs;
xs.push_back(0);
for (int a = 0, b; a < d; a = b) {
const int k = d / (a + 1);
b = d / k;
xs.push_back(b - 1);
}
const int mid = xs.size();
for (int a = 0, b; a < d - 1; a = b) {
const int k = (d - 1) / (a + 1) + 1;
b = (d - 1) / (k - 1);
xs.push_back(b);
}
xs.push_back(N);
inplace_merge(xs.begin(), xs.begin() + mid, xs.end());
// cerr<<"d = "<<d<<": xs = "<<xs<<endl;
for (int i = 0; i < (int)xs.size(); ++i) if (i || xs[i - 1] < xs[i]) {
// (xs[i - 1], xs[i]]
const int x = xs[i];
const int L = d / (x + 1) + 1;
const int R = x ? ((d + x - 1) / x - 1) : N;
if (L <= R) {
path[d] -= (i ? Mint(xs[i] - xs[i - 1]) : 1) * Mint((Int)(R - L + 1) * (R - L + 2) / 2);
}
}
}
// cerr<<"N = "<<N<<": path = "<<path<<endl;
for (int d = 1; d <= N - 1; ++d) path[d] += path[d - 1];
vector<Mint> ws(N + 1);
ws[N] = 1;
for (int n = N; --n >= 0; ) ws[n] = ws[n + 1] * N;
for (int n = 0; n <= N; ++n) ws[n] *= fac[N] * invFac[N - n];
ws[0] = 0;
for (int n = 1; n <= N; ++n) ws[n] += ws[n - 1];
auto get = [&](int nL, int nR) -> Mint {
return (nL <= nR) ? (ws[nR] - ws[nL - 1]) : 0;
};
Mint ans = 0;
// before cycle
for (int h = 1; h <= N - 1; ++h) {
ans += get(h + 1, N) * path[h - 1];
}
// cycle
vector<Mint> fs(N + 1, 0), gs(N + 1, 1);
for (int m = 1; m <= N; ++m) {
const Mint w = get(m, N);
/*
Int sum = 0;
for (int L = 1; L <= N; ++L) sum += m / __gcd(L, m);
ans += w * sum;
*/
fs[m] += w * Mint(m);
ans += w * Mint((Int)N * (N - 1) / 2) * Mint(m);
}
// gcd conv
for (int i = 1; i <= N; ++i) for (int j = 2 * i; j <= N; j += i) fs[i] += fs[j];
for (int i = 1; i <= N; ++i) for (int j = 2 * i; j <= N; j += i) gs[i] += gs[j];
for (int i = 1; i <= N; ++i) fs[i] *= gs[i];
for (int i = N; i >= 1; --i) for (int j = 2 * i; j <= N; j += i) fs[i] -= fs[j];
for (int i = 1; i <= N; ++i) ans += fs[i] * inv[i];
// S = T
ans -= Mint(N).pow(N) * Mint((Int)N * (N + 1) / 2) * N;
return ans;
}
int main() {
int N, P;
for (; ~scanf("%d%d", &N, &P); ) {
Mint::setM(P);
prepare();
const Mint ans = fast(N);
printf("%u\n", ans.x);
#ifdef LOCAL
/*
const Mint slw=slow(N);
const Mint slw2=slow2(N);
cerr<<"slw = "<<slw<<endl;
cerr<<"slw2 = "<<slw2<<endl;
//*/
#endif
}
return 0;
}