結果

問題 No.2206 Popcount Sum 2
ユーザー siro53
提出日時 2023-02-04 00:34:22
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 796 ms / 4,000 ms
コード長 5,678 bytes
コンパイル時間 2,163 ms
コンパイル使用メモリ 200,524 KB
最終ジャッジ日時 2025-02-10 10:22:17
ジャッジサーバーID
(参考情報)
judge3 / judge1
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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

#line 1 "combined.cpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
template <class T> inline bool chmax(T &a, T b) {
if(a < b) {
a = b;
return 1;
}
return 0;
}
template <class T> inline bool chmin(T &a, T b) {
if(a > b) {
a = b;
return 1;
}
return 0;
}
#ifdef DEBUG
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
os << '{';
for(int i = 0; i < (int)v.size(); i++) {
if(i) { os << ','; }
os << v[i];
}
os << '}';
return os;
}
void debugg() { cerr << endl; }
template <class T, class... Args>
void debugg(const T &x, const Args &... args) {
cerr << " " << x;
debugg(args...);
}
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debugg(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
struct Setup {
Setup() {
cin.tie(0);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} __Setup;
using ll = long long;
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define REP1(i, n) for(int i = 0; i < int(n); i++)
#define REP2(i, a, b) for(int i = (a); i < int(b); i++)
#define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) ((int)(v).size())
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
constexpr int MOD = 1000000007;
constexpr int MOD2 = 998244353;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
void Case(int i) { cout << "Case #" << i << ": "; }
int popcount(int x) { return __builtin_popcount(x); }
ll popcount(ll x) { return __builtin_popcountll(x); }
#pragma endregion Macros
#line 1 "/Users/cbiolab/kyo-pro/compro_library/math/modint.hpp"
template <int mod> struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod)
x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod)
x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inv();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inv() const {
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1)
ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt<mod>(t);
return (is);
}
static int get_mod() { return mod; }
};
#line 77 "combined.cpp"
using mint = ModInt<MOD2>;
#line 1 "/Users/cbiolab/kyo-pro/compro_library/math/combination.hpp"
struct Combination {
int MAX;
vector<mint> fac, finv;
Combination(int _MAX) : fac(_MAX), finv(_MAX), MAX(_MAX) {
fac[0] = fac[1] = 1;
for(int i = 2; i < MAX; i++) { fac[i] = fac[i - 1] * i; }
finv[MAX - 1] = fac[MAX - 1].inv();
for(int i = MAX - 1; i >= 1; i--) { finv[i - 1] = finv[i] * i; }
}
mint COM(int n, int k) {
if(n < k || n < 0 || k < 0) { return 0; }
return fac[n] * finv[k] * finv[n - k];
}
};
#line 80 "combined.cpp"
Combination comb(300010);
/*
(2^N-1) * sum_{i=0}^{M-1} C(N-1, i)
f(n, m) = sum_{i=0}^{m} C(n, i)
f(n, m+1) = f(n, m) + C(n, m+1)
f(n, m-1) = f(n, m) - C(n, m)
f(n+1, m) = f(n, m) * 2 - C(n, m)
f(n-1, m) = (f(n, m) + C(n-1, m)) / 2
*/
const int B = 512;
vector<mint> pre[400];
int main() {
for(int k = 1; k < 400; k++) {
int n = k * B;
pre[k].resize(n + 1);
pre[k][0] = 1;
REP(m, 1, n+1) pre[k][m] = pre[k][m-1] + comb.COM(n, m);
}
int T;
cin >> T;
mint inv2 = mint(2).inv();
REP(_, T) {
int N, M;
cin >> N >> M;
mint ans = 0;
if(N <= B) {
REP(i, M) ans += comb.COM(N-1, i);
} else {
int pos = (N-1+B-1) / B;
assert(1 <= pos and pos < 400);
assert(SZ(pre[pos]) > M-1);
assert(pos*B >= N-1);
ans = pre[pos][M-1];
REP(i, pos*B - (N-1)) ans = (ans + comb.COM(pos*B-i-1, M-1)) * inv2;
}
ans *= mint(2).pow(N) - 1;
cout << ans << '\n';
}
}
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