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Problem 2282 Wand

Accept: 432 Submit: 1537
Time Limit: 1000 mSec Memory Limit : 262144 KB

Problem Description

N wizards are attending a meeting. Everyone has his own magic wand. N magic wands was put in a line, numbered from 1 to n(Wand_i owned by wizard_i). After the meeting, n wizards will take a wand one by one in the order of 1 to n. A boring wizard decided to reorder the wands. He is wondering how many ways to reorder the wands so that at least k wizards can get his own wand.

For example, n=3. Initially, the wands are w1 w2 w3. After reordering, the wands become w2 w1 w3. So, wizard 1 will take w2, wizard 2 will take w1, wizard 3 will take w3, only wizard 3 get his own wand.

Input

First line contains an integer T (1 ≤ T ≤ 10), represents there are T test cases.

For each test case: Two number n and k.

1<=n <=10000.1<=k<=100. k<=n.

Output

For each test case, output the answer mod 1000000007(10^9 + 7).

Sample Input

2 1 1 3 1

Sample Output

1 4

Source

第八屆福建省大學生程序設計競賽-重現賽（感謝承辦方廈門理工學院） 題意：有n個法師n根魔法棒,每個法師都有屬於自己的1根魔法棒，求至少有k個法師沒拿到自己的魔法棒的情況數。 思路：首先題目中k遠遠小於n，所以可以考慮相反面，考慮只有1,2,...,k-1個法師沒拿到自己的魔法棒的情況數，再用n!減去這些情況的情況數即可。 若挑出x個人，這x個人都沒拿到自己的魔法棒的情況數記為D(x),即為數量為x個人的錯排數，C(n,x)*D(x)就是x個人沒拿到魔法棒的總情況數。 AC代碼：

#define
 
 _CRT_SECURE_NO_DEPRECATE
#include <iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<bitset>
#include<set>
#include<map>
#include<cmath>
#include<queue>
using namespace std;
#define N_MAX 10000+4
#define MOD 1000000007
#define INF 0x3f3f3f3f
typedef long long ll;
int n, k;
ll dp[N_MAX];//錯排數
ll C[N_MAX][100 + 2];
void init() {
    dp[0] = 1; dp[1] = 0; dp[2] = 1;
    for (int i = 3; i < N_MAX; i++) {
        dp[i] = ((i - 1)*(dp[i - 1] + dp[i - 2]) + MOD) % MOD;
    }
}
void C_table() {
    for (int i = 0; i < N_MAX; i++) {
        C[i][0] = 1;
        for (int j = 1; j <= min(100, i); j++) {//!!!
            C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % MOD;
        }
    }
}

int main() {
    init(); C_table();
    int t; scanf("%d", &t);
    while (t--) {
        scanf("%d%d", &n, &k);
        ll num = 0, ans = 1;
        for (ll i = 1; i <= n; i++) {
            ans = ans*i%MOD;
        }
        for (int i = 0; i <= k - 1; i++) {
            num = (num + C[n][i] * dp[n - i]) % MOD;
        }
        printf("%lld\n", (ans - num + MOD) % MOD);
    }
    return 0;
}

foj Problem 2282 Wand