結果

問題 No.503 配列コレクション
ユーザー parukiparuki
提出日時 2017-04-07 23:35:42
言語 C++14
(gcc 10.1.0 + boost 1.73.0)
結果
AC  
実行時間 15 ms / 2,000 ms
コード長 3,251 Byte
コンパイル時間 1,504 ms
使用メモリ 5,316 KB
最終ジャッジ日時 2020-06-29 03:37:47

テストケース

テストケース表示
入力 結果 実行時間
使用メモリ
testcase_00 AC 3 ms
1,584 KB
testcase_01 AC 2 ms
1,576 KB
testcase_02 AC 2 ms
1,640 KB
testcase_03 AC 2 ms
1,584 KB
testcase_04 AC 2 ms
1,584 KB
testcase_05 AC 2 ms
1,588 KB
testcase_06 AC 2 ms
1,612 KB
testcase_07 AC 3 ms
1,588 KB
testcase_08 AC 2 ms
1,624 KB
testcase_09 AC 3 ms
1,612 KB
testcase_10 AC 3 ms
1,884 KB
testcase_11 AC 10 ms
4,784 KB
testcase_12 AC 9 ms
4,784 KB
testcase_13 AC 4 ms
2,676 KB
testcase_14 AC 6 ms
3,200 KB
testcase_15 AC 8 ms
4,520 KB
testcase_16 AC 11 ms
5,312 KB
testcase_17 AC 9 ms
4,260 KB
testcase_18 AC 10 ms
5,052 KB
testcase_19 AC 15 ms
5,312 KB
testcase_20 AC 11 ms
5,312 KB
testcase_21 AC 3 ms
1,584 KB
testcase_22 AC 6 ms
2,940 KB
testcase_23 AC 2 ms
1,576 KB
testcase_24 AC 11 ms
5,316 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 #
#include "bits/stdc++.h"
using namespace std;
#define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i))
#define rep(i,j) FOR(i,0,j)
#define each(x,y) for(auto &(x):(y))
#define mp make_pair
#define mt make_tuple
#define all(x) (x).begin(),(x).end()
#define debug(x) cout<<#x<<": "<<(x)<<endl
#define smax(x,y) (x)=max((x),(y))
#define smin(x,y) (x)=min((x),(y))
#define MEM(x,y) memset((x),(y),sizeof (x))
#define sz(x) (int)(x).size()
#define pb push_back
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;

template<int MOD>
class ModInt {
public:
    ModInt() :value(0) {}
    ModInt(long long val) :value((int)(val<0 ? MOD + val%MOD : val%MOD)) { }

    ModInt& operator+=(ModInt that) {
        value = value + that.value;
        if (value >= MOD)value -= MOD;
        return *this;
    }
    ModInt& operator-=(ModInt that) {
        value -= that.value;
        if (value<0)value += MOD;
        return *this;
    }
    ModInt& operator*=(ModInt that) {
        value = (int)((long long)value * that.value % MOD);
        return *this;
    }
    ModInt &operator/=(ModInt that) {
        return *this *= that.inverse();
    }
    ModInt operator+(ModInt that) const {
        return ModInt(*this) += that;
    }
    ModInt operator-(ModInt that) const {
        return ModInt(*this) -= that;
    }
    ModInt operator*(ModInt that) const {
        return ModInt(*this) *= that;
    }
    ModInt operator/(ModInt that) const {
        return ModInt(*this) /= that;
    }
    ModInt pow(long long k) const {
        if (value == 0)return 0;
        ModInt n = *this, res = 1;
        while (k) {
            if (k & 1)res *= n;
            n *= n;
            k >>= 1;
        }
        return res;
    }
    ModInt inverse() const {
        long long a = value, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        return ModInt(u);
    }
    int toi() const { return value; }

private:
    int value;
};
typedef ModInt<1000000007> mint;
ostream& operator<<(ostream& os, const mint& x) {
    os << x.toi();
    return os;
}

mint nPr(int n, int r, const vector<mint> &fact) {
    return fact[n] / fact[n - r];
}
mint nCr(int n, int r, const vector<mint> &fact) {
    if (r > n)return 0;
    return fact[n] / (fact[r] * fact[n - r]);
}
mint nHr(int n, int r, const vector<mint> &fact) {
    return nCr(n + r - 1, r, fact);
}

/*

r-1+k-1<k
r-2<0
r<2
*/

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);

    int N, K, D;
    cin >> N >> K >> D;

    vector<mint> fact(N + 1, 1);
    rep(i, N)fact[i + 1] = fact[i] * (i + 1);

    int m = 0, r = N;
    while (r >= K) {
        r -= K - 1;
        m++;
    }

    if (D == 1) {
        // {1,1,1,...,1}
        cout << r << endl;
        return 0;
    }

    if (r == 1) {
        mint ans = 1;
        rep(i, m)ans *= D;
        cout << ans << endl;
        return 0;
    }

    mint ans = 0, pw = 1;
    for (int i = 0; i <= m; ++i) {
        int k = m - i;
        if (!(r - 1 == 0 && k > 0)) {
            ans += nHr(r - 1, k, fact)*pw*r;
        }
        pw *= D;
    }
    cout << ans << endl;
}
0