結果

問題 No.2206 Popcount Sum 2
ユーザー nononnonon
提出日時 2024-12-04 10:16:04
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,316 ms / 4,000 ms
コード長 5,838 bytes
コンパイル時間 3,406 ms
コンパイル使用メモリ 255,972 KB
実行使用メモリ 5,952 KB
最終ジャッジ日時 2024-12-04 10:16:33
合計ジャッジ時間 28,480 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
このコードへのチャレンジ
(要ログイン)
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 <bits/stdc++.h>
using namespace std;
template<int MOD>
struct modint {
modint() : x(0) {}
modint(long long v) {
long long y = v % m();
if (y < 0) y += m();
x = (unsigned int)(y);
}
static modint raw(int v) {
modint a;
a.x = v;
return a;
}
static constexpr int mod() { return m(); }
unsigned int val() const { return x; }
modint& operator++() {
x++;
if (x == m()) x = 0;
return *this;
}
modint& operator--() {
if (x == 0) x = m();
x--;
return *this;
}
modint operator++(int) {
modint res = *this;
++*this;
return res;
}
modint operator--(int) {
modint res = *this;
--*this;
return res;
}
modint& operator+=(const modint &r) {
x += r.x;
if (x >= m()) x -= m();
return *this;
}
modint& operator-=(const modint &r) {
x -= r.x;
if (x >= m()) x += m();
return *this;
}
modint& operator*=(const modint &r) {
unsigned long long y = x;
y *= r.x;
x = (unsigned int)(y % m());
return *this;
}
modint &operator/=(const modint &r) {
return *this = *this * r.inv();
}
friend modint operator+(const modint &a, const modint &b) {
return modint(a) += b;
}
friend modint operator-(const modint &a, const modint &b) {
return modint(a) -= b;
}
friend modint operator*(const modint &a, const modint &b) {
return modint(a) *= b;
}
friend modint operator/(const modint &a, const modint &b) {
return modint(a) /= b;
}
friend bool operator==(const modint &a, const modint &b) {
return a.x == b.x;
}
friend bool operator!=(const modint &a, const modint &b) {
return a.x != b.x;
}
modint operator+() const { return *this; }
modint operator-() const { return modint() - *this; }
modint pow(long long k) const {
assert(k >= 0);
modint a = *this;
modint res = 1;
while (k > 0) {
if (k & 1) res *= a;
a *= a;
k >>= 1;
}
return res;
}
modint inv() const {
long long a = x, b = m(), u = 1, v = 0;
while (b > 0) {
long long t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
return modint(u);
}
private:
unsigned int x;
static constexpr unsigned int m() { return MOD; }
};
template<typename mint>
struct combination {
combination(int n = 0) { init(n); }
mint fac(int n) {
init(n);
return inner_fac[n];
}
mint finv(int n) {
init(n);
return inner_finv[n];
}
mint inv(int n) {
assert(n > 0);
init(n);
return inner_finv[n] * inner_fac[n - 1];
}
mint C(int n, int k) {
if (k < 0) return 0;
if (n < 0) {
int sgn = (k & 1 ? -1 : 1);
return sgn * C(k - n - 1, k);
}
if (n < k) return 0;
if (n < min(1 << 25, mint::mod() - 1)) {
init(n);
return inner_fac[n] * inner_finv[n - k] * inner_finv[k];
}
init(k);
mint res = inner_finv[k];
for (int i = 0; i < k; i++) res *= n - i;
return res;
}
mint P(int n, int k) {
if (n < 0 || k < 0 || n < k) return 0;
return inner_fac[n] * inner_finv[n - k];
}
mint catalan(int n) {
init(2 * n);
return inner_fac[2 * n] * inner_finv[n] * inner_finv[n + 1];
}
private:
static vector<mint> inner_fac, inner_finv;
static void init(int n) {
int sz = inner_fac.size();
if (n < sz) return;
n = clamp(n, 2 * sz, min(1 << 25, mint::mod() - 1));
inner_fac.resize(n + 1);
inner_finv.resize(n + 1);
for (int i = sz; i <= n; i++) {
inner_fac[i] = i * inner_fac[i - 1];
}
inner_finv[n] = inner_fac[n].inv();
for (int i = n; i >= sz; i--) {
inner_finv[i - 1] = i * inner_finv[i];
}
}
};
template<typename mint>
vector<mint> combination<mint>::inner_fac(1, 1);
template<typename mint>
vector<mint> combination<mint>::inner_finv(1, 1);
template<typename mint>
struct prefix_binomial_sum {
prefix_binomial_sum(int n) : size(n), b(400) { build(); }
mint get(int n, int k) const {
assert(0 <= n && n <= size);
int tn = (n + b / 2) / b;
int tk = (k + b / 2) / b;
mint res = table[tn][tk];
tn *= b;
tk *= b;
while (tk < k) res = res + C.C(tn, ++tk);
while (tk > k) res = res - C.C(tn, tk--);
while (tn < n) res = 2 * res - C.C(tn++, tk);
while (tn > n) res = (res + C.C(--tn, tk)) * inv2;
return res;
}
private:
int size, b;
mint inv2;
vector<vector<mint>> table;
static combination<mint> C;
void build() {
size += b;
inv2 = mint::raw(2).inv();
int n = (size + b - 1) / b;
table.resize(n + 1);
for (int i = 0; i <= n; i++) {
table[i].resize(n + 1);
table[i][0] = 1;
mint cur = 1;
for (int j = 1; j <= n * b; j++) {
cur += C.C(b * i, j);
if (j % b == 0) {
table[i][j / b] = cur;
}
}
}
}
};
using mint = modint<998244353>;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
cin >> T;
prefix_binomial_sum<mint> C((int)2e5);
while (T--) {
int N, M;
cin >> N >> M;
mint ans = mint(2).pow(N) - 1;
ans *= C.get(N - 1, M - 1);
cout << ans.val() << '\n';
}
}
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