結果

問題 No.1785 Inequality Signs
コンテスト
ユーザー 8UqsVg4r
提出日時 2021-12-12 22:14:03
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 79 ms / 2,000 ms
コード長 8,107 bytes
コンパイル時間 3,900 ms
コンパイル使用メモリ 243,308 KB
実行使用メモリ 15,348 KB
最終ジャッジ日時 2024-07-22 23:27:57
合計ジャッジ時間 7,499 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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ファイルパターン 結果
sample AC * 2
other AC * 52
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ソースコード

diff # 

//////___/_/////////////////////////////////_////____//__////
//  / ___(_)_   _____   _ __ ___   ___     / \  / ___| | | //
// | |  _| \ \ / / _ \ | '_ ` _ \ / _ \   / _ \| |     | | //
// | |_| | |\ V /  __/ | | | | | |  __/  / ___ \ |___  |_| //
//  \____|_| \_/ \___| |_| |_| |_|\___| /_/   \_\____| (_) //
///////////////////////////////////////////////////////////
#include <bits/stdc++.h>
#include <type_traits>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
#define Sugsugar cin.tie(0);ios::sync_with_stdio(false)
extern const ll MOD;
const ll INF = (ll)2e16;
const int Inf = 2e9;
const int MAX = 500000;
const ld PI = (acos(-1));
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true;} return false;}
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true;} return false;}
ld rad(ld a) {return a * PI / 180.0;}
const int dx[8] = {1, 0, -1, 0, -1, 1, -1, 1};//2次元グリッド上のx軸方向
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};//2次元グリッド上のy軸方向
template<class T> void rm(vector<T> &vec) {vec.erase(unique(vec.begin(), vec.end()), vec.end());}
void rm(string &vec) {vec.erase(unique(vec.begin(), vec.end()), vec.end());}
struct UnionFind {
    vector<int> par;
    
    UnionFind(int n) : par(n, -1) { }
 
    int root(int x) {
        if (par[x] < 0) return x;
        else return par[x] = root(par[x]);
    }
    
    bool same(int x, int y) {
        return root(x) == root(y);
    }
    
    bool merge(int x, int y) {
        x = root(x); y = root(y);
        if (x == y) return false;
        if (par[x] > par[y]) swap(x, y); // merge technique
        par[x] += par[y];
        par[y] = x;
        return true;
    }
    
    int size(int x) {
        return -par[root(x)];
    }
};

template <typename T>
struct BIT {
    int n;          // 配列の要素数(数列の要素数+1)
    vector<T> bit;  // データの格納先
    BIT(int n_) : n(n_ + 1), bit(n, 0) {}
    void add(int i, T x) {
        for (int idx = i; idx < n; idx += (idx & -idx)) {
            bit[idx] += x;
        }
    }
    T sum(int i) {
        T s(0);
        for (int idx = i; idx > 0; idx -= (idx & -idx)) {
            s += bit[idx];
        }
        return s;
    }
};


 
vector<pair<ll, ll>> factorize(ll N) {
    vector<pair<ll, ll>> res;
    for (ll a = 2; a * a <= N; ++a) {
        if (N % a != 0) continue;
        ll ex = 0; // 指数

        // 割れる限り割り続ける
        while (N % a == 0) {
            ++ex;
            N /= a;
        }

        // その結果を push
        res.push_back({a, ex});
    }

    // 最後に残った数について
    if (N != 1) res.push_back({N, 1});
    return res;
}
 
ll mod(ll val,ll md = MOD) {
  ll res = val % md;
  if (res < 0) res += md;
  return res;
}
 
char upper(char c){
    if('a' <= c && c <= 'z'){
        c = c - ('a' - 'A');
    }
    return c;
}
char lower(char c){
    if('A' <= c && c <= 'Z'){
        c = c + ('a' - 'A');
    }
    return c;
}

ll fac[MAX], finv[MAX], inv[MAX];

void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}

// 二項係数計算
ll COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

ll Expo(ll N,ll K,ll md = MOD) {
    if (md == 0) {
        ll sum = 1;
        for (int i = 0; i < K; i++) sum *= N;
        return sum;
    }
    if (md == 1) return 0;
    N %= md;
    if (K == 0) {
        return 1;
    }
    ll Kc = K,rui = N,ans = 1;
    while(Kc) {
        if (Kc % 2) {
            ans *= rui;
            ans %= md;
        }
        rui *= rui;
        rui %= md;
        Kc /= 2;
    }
    return ans;
}

ll extGCD(ll a, ll b, ll &x, ll &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    ll d = extGCD(b, a%b, y, x); // 再帰的に解く
    y -= a / b * x;
    return d;
}

template<class T>
constexpr auto unit() -> enable_if_t<is_integral<T>::value, T> {
	return 1;
}
template<class T>
constexpr auto unit() -> enable_if_t<is_floating_point<T>::value, T> {
	return 1e-14;
}

template<class T> T sqroot(T Ex) {
    T l = 0,r = min(Ex,(T)(1e9));
    while (r - l > unit<T>()) {
        T val = (l + r) / 2;
        if (val * val > Ex) r = val;
        else l = val;
    }
    return l;//Ex以下のT型の平方根
}

template<class T> void sitpress(vector<T> &vec) {
    vector<T> array = vec;
    sort(array.begin(),array.end());
    rm(array);
    for (int i = 0; i < vec.size(); i++) {
        int l = -1,r = array.size();
        while (r - l > 1) {
            int mid = (l + r) / 2;
            if (array.at(mid) >= vec.at(i)) r = mid;
            else l = mid;
        }
        vec.at(i) = r;
    }
}

template<class T> ll Rolling(vector<T> Girl) {
    BIT<int> RG(Girl.size());
    int si = Girl.size();
    ll gl = 0;
    sitpress(Girl);
    for (int i = 0; i < si; i++) {
        Girl.at(i)++;
        gl += RG.sum(si) - RG.sum(Girl.at(i));
        RG.add(Girl.at(i),1);
    }
    return gl;
}

vector<vector<ll>> mat(vector<vector<ll>> a, vector<vector<ll>> b) {
    assert(a.at(0).size() == b.size());
    int l = a.size(),m = b.size(),n = b.at(0).size();
    vector<vector<ll>> c(l,vector<ll>(n,0));
    for (int i = 0; i < l; i++) {
        for (int j = 0; j < n; j++) {
            for (int k = 0; k < m; k++) {
                c.at(i).at(j) += a.at(i).at(k) * b.at(k).at(j) % MOD;
                c.at(i).at(j) %= MOD;
            }
        }
    }
    a = c;
    return c;
}

vector<vector<ll>> matpower(vector<vector<ll>> a,ll bit) { //この行列は正方行列のみ
    vector<vector<ll>> ans(a.size(),vector<ll>(a.size()));
    bool hoge = true;
    for (int i = 0; i <= 62; i++) {
        if ((bit >> i) & 1) {
            if (hoge) {
                ans = a;
                hoge = false;
            }
            else {
                ans = mat(ans,a);
            }
        }
        a = mat(a,a);
    }
    return ans;
}

vector<ll> OneHeart(vector<ll> X,vector<ll> Y) {
    ll denom = 2 * (X[2] * Y[1] - X[1] * Y[2] + X[0] * Y[2] - X[2] * Y[0] + X[1] * Y[0] - X[0] * Y[1]);
    ll Numer = Y[0] * (X[2] * X[2] + Y[2] * Y[2] - X[1] * X[1] - Y[1] * Y[1]);
    Numer += Y[1] * (X[0] * X[0] + Y[0] * Y[0] - X[2] * X[2] - Y[2] * Y[2]);
    Numer += Y[2] * (X[1] * X[1] + Y[1] * Y[1] - X[0] * X[0] - Y[0] * Y[0]);
    if (denom == 0) {
        vector<ll> Cor{-INF,-INF};
        return Cor;
    }
    Numer *= -1;
    if (denom * Numer >= 0) {
        chmax(denom,-denom);
        chmax(Numer,-Numer);
    }
    else {
        chmax(denom,-denom);
        chmin(Numer,-Numer);
    }
    vector<ll> Cor{Numer,denom};
    return Cor;
}

vector<vector<ll>> OutHeart(vector<ll> X, vector<ll> Y){
    vector<vector<ll>> OutH(2,vector<ll>(2));
    OutH.at(0) = OneHeart(X,Y);
    OutH.at(1) = OneHeart(Y,X);
    return OutH;
}

struct edge {ll to,cost;};
template<class T> using Graph = vector<vector<T>>;

const ll MOD = 1e9+7;

/*
random_device seed;
default_random_engine engine(seed());
uniform_int_distribution<ll> num(x,y);
*/

int main(){
    Sugsugar;
    COMinit();
    ll N, K;
    cin >> N >> K;
    ll sum = 1;
    for (ll i = 1; i <= N; i++) {
        sum *= K - i + 1;
        sum %= MOD;
        sum *= Expo(i, MOD - 2);
        sum %= MOD;
    }
    if (K < N) sum = 0;
    ll ans = 0;
    bool flag = false;
    for (ll i = 0; i <= N; i++) {
        ans += sum * COM(N - 1, i) % MOD;
        ans %= MOD;
        if (flag || N <= K) {
            sum *= K + i + 1;
            sum %= MOD;
            sum *= Expo(K - N + i + 1, MOD - 2);
            sum %= MOD;
        }
        else if (K + i + 1 == N && !flag) {
            flag = true;
            sum = 1;
        }
    }
    cout << ans << endl;
    return 0;
}
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