結果

問題 No.2206 Popcount Sum 2
ユーザー 👑 hos.lyric
提出日時 2023-02-03 21:48:01
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 541 ms / 4,000 ms
コード長 6,063 bytes
コンパイル時間 1,401 ms
コンパイル使用メモリ 110,964 KB
実行使用メモリ 11,264 KB
最終ジャッジ日時 2024-07-02 19:40:23
合計ジャッジ時間 8,425 ms
ジャッジサーバーID
(参考情報)
judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 18
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#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 <map>
#include <numeric>
#include <queue>
#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; }
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr 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) { x = (static_cast<unsigned long long>(x) * a.x) % 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; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
constexpr int LIM_INV = 400'010;
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;
}
}
}
int T;
vector<int> N, M;
int main() {
prepare();
for (; ~scanf("%d", &T); ) {
N.resize(T);
M.resize(T);
for (int t = 0; t < T; ++t) {
scanf("%d%d", &N[t], &M[t]);
}
vector<Mint> ans(T);
for (int t = 0; t < T; ++t) {
ans[t] = Mint(2).pow(N[t]) - 1;
--N[t];
--M[t];
}
const int maxN = *max_element(N.begin(), N.end());
const int B = max((int)(maxN / sqrt(T)), 1);
vector<int> ts(T);
for (int t = 0; t < T; ++t) {
ts[t] = t;
}
sort(ts.begin(), ts.end(), [&](int t0, int t1) -> bool {
const int xa = M[t0] / B;
const int xb = M[t1] / B;
return ((xa != xb) ? (xa < xb) : (xa & 1) ? (N[t0] > N[t1]) : (N[t0] < N[t1]));
});
Mint x = 1, y = 1;
int m = 0, n = 0;
for (int q = 0; q < T; ++q) {
const int t = ts[q];
for (; m > M[t]; ) {
--m;
x -= y;
y *= inv[n - m] * (m + 1);
// cerr<<__LINE__<<"; "<<n<<" "<<m<<" "<<x<<" "<<y<<endl;
}
for (; n < N[t]; ) {
x = 2 * x - y;
y *= (n + 1) * inv[n - m + 1];
++n;
// cerr<<__LINE__<<"; "<<n<<" "<<m<<" "<<x<<" "<<y<<endl;
}
for (; m < M[t]; ) {
y *= (n - m) * inv[m + 1];
x += y;
++m;
// cerr<<__LINE__<<"; "<<n<<" "<<m<<" "<<x<<" "<<y<<endl;
}
for (; n > N[t]; ) {
--n;
y *= inv[n + 1] * (n - m + 1);
x = inv[2] * (x + y);
// cerr<<__LINE__<<"; "<<n<<" "<<m<<" "<<x<<" "<<y<<endl;
}
ans[t] *= x;
}
for (int t = 0; t < T; ++t) {
printf("%u\n", ans[t].x);
}
}
return 0;
}
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