## Source

### Problem

Passwords are widely used in our lives: for ATMs, online forum logins, mobile device unlock and door access. Everyone cares about password security. However, attackers always find ways to steal our passwords. Here is one possible situation:

Assume that Eve, the attacker, wants to steal a password from the victim Alice. Eve cleans up the keyboard beforehand. After Alice types the password and leaves, Eve collects the fingerprints on the keyboard. Now she knows which keys are used in the password. However, Eve won't know how many times each key has been pressed or the order of the keystroke sequence.

To simplify the problem, let's assume that Eve finds Alice's fingerprints only occurs on M keys. And she knows, by another method, that Alice's password contains N characters. Furthermore, every keystroke on the keyboard only generates a single, unique character. Also, Alice won't press other irrelevant keys like 'left', 'home', 'backspace' and etc.

Here's an example. Assume that Eve finds Alice's fingerprints on M=3 key '3', '7' and '5', and she knows that Alice's password is N=4-digit in length. So all the following passwords are possible: 3577, 3557, 7353 and 5735. (And, in fact, there are 32 more possible passwords.)

However, these passwords are not possible:

1357  // There is no fingerprint on key '1'
3355  // There is fingerprint on key '7',
so '7' must occur at least once.
357   // Eve knows the password must be a 4-digit number.


With the information, please count that how many possible passwords satisfy the statements above. Since the result could be large, please output the answer modulo 1000000007(109+7).

#### Input

The first line of the input gives the number of test cases, T. For the next T lines, each contains two space-separated numbers M and N, indicating a test case.

#### Output

For each test case, output one line containing "Case #x: y", where x is the test case number (starting from 1) and y is the total number of possible passwords modulo 1000000007(109+7).

#### Limits

Small dataset

T = 15. 1 ≤ M ≤ N ≤ 7.

Large dataset

T = 100. 1 ≤ M ≤ N ≤ 100.

#### Smaple

Input    Output

4
1 1      Case #1: 1
3 4      Case #2: 36
5 5      Case #3: 120
15 15    Case #4: 674358851


## 题解

dp[i][j] = dp[m][n-1] * m + dp[m - 1][n - 1] * m


### Java

import java.util.*;

public class Solution {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
int T = in.nextInt();
// System.out.println("T = " + T);
for (int t = 1; t <= T; t++) {
int M = in.nextInt(), N = in.nextInt();
long ans = solve(M, N);
// System.out.printf("M = %d, N = %d\n", M, N);
System.out.printf("Case #%d: %d\n", t, ans);
}
}

public static long solve(int M, int N) {
long[][] dp = new long[1 + M][1 + N];
long mod = 1000000007;
for (int j = 1; j <= N; j++) {
dp[1][j] = 1;
}
for (int i = 2; i <= M; i++) {
for (int j = i; j <= N; j++) {
dp[i][j] = i * (dp[i][j - 1] + dp[i - 1][j - 1]);
dp[i][j] %= mod;
}
}

return dp[M][N];
}
}


### 源码分析

Google Code Jam 上都是自己下载输入文件，上传结果，这里我们使用输入输出重定向的方法解决这个问题。举个例子，将这段代码保存为Solution.java, 将标准输入重定向至输入文件，标准输出重定向至输出文件。编译好之后以如下方式运行：

java Solution < A-large-practice.in > A-large-practice.out