結果

問題 No.2206 Popcount Sum 2
ユーザー siro53siro53
提出日時 2023-02-04 00:34:22
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 747 ms / 4,000 ms
コード長 5,678 bytes
コンパイル時間 2,393 ms
コンパイル使用メモリ 205,212 KB
実行使用メモリ 166,048 KB
最終ジャッジ日時 2023-09-15 20:56:54
合計ジャッジ時間 17,529 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge12
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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 282 ms
166,000 KB
testcase_01 AC 284 ms
165,992 KB
testcase_02 AC 285 ms
165,744 KB
testcase_03 AC 285 ms
166,048 KB
testcase_04 AC 287 ms
166,024 KB
testcase_05 AC 741 ms
165,756 KB
testcase_06 AC 746 ms
165,996 KB
testcase_07 AC 744 ms
165,940 KB
testcase_08 AC 747 ms
165,724 KB
testcase_09 AC 747 ms
165,776 KB
testcase_10 AC 731 ms
165,876 KB
testcase_11 AC 724 ms
165,796 KB
testcase_12 AC 722 ms
166,016 KB
testcase_13 AC 716 ms
165,772 KB
testcase_14 AC 715 ms
165,800 KB
testcase_15 AC 715 ms
165,744 KB
testcase_16 AC 714 ms
165,724 KB
testcase_17 AC 720 ms
165,860 KB
testcase_18 AC 718 ms
165,752 KB
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 # 

#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);
/*
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';
    } 
}
0