結果
問題 | No.2206 Popcount Sum 2 |
ユーザー |
|
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 |
ソースコード
#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 DEBUGtemplate <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))#endifstruct 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);/*答えは (2^N-1) * sum_{i=0}^{M-1} C(N-1, i)f(n, m) = sum_{i=0}^{m} C(n, i) とすると、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';}}