#include <bits/stdc++.h>
#pragma GCC optime(3)
#pragma GCC optime(2)
#pragma GCC optime(1)
using namespace std;
long long n, k, t;
long long ans, a[1001], b[1001][1001], dp[1001][1001];
const long long mod = 1e9 + 7;
signed main() {
  for (register long long i = 0; i <= 1000; ++i) {
    b[i][0] = 1;
    for (register long long j = 1; j <= i; ++j)
      b[i][j] = (b[i - 1][j] + b[i - 1][j - 1]) % mod;
  }
  dp[1][1] = 1;
  a[0] = 1;
  for (register long long i = 1; i <= 1000; ++i) {
    a[i] = a[i - 1] * i % mod;
    for (register long long j = 1; j <= i; ++j) {
      if (i + j < 1001) dp[i + j][j] = (dp[i + j][j] + dp[i][j]) % mod;
      if (i + j < 1000)
        dp[i + j + 1][j + 1] = (dp[i + j + 1][j + 1] + dp[i][j]) % mod;
    }
  }
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d", &n, &k);
    ans = 0;
    for (register long long i = k; i <= n; ++i)
      ans = (ans + dp[i][k] * b[n - i + k][k] % mod * a[k]) % mod;
    printf("%d\n", ans);
  }
  return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

The sequence of integer pairs (a1, b1), (a2, b2), ..., (ak, bk) is beautiful, if the following statements are fulfilled: 

  * 1 ≤ a1 ≤ b1 < a2 ≤ b2 < ... < ak ≤ bk ≤ n, where n is a given positive integer; 
  * all numbers b1 - a1, b2 - a2, ..., bk - ak are distinct. 



For the given number n find the number of beautiful sequences of length k. As the answer can be rather large, print the remainder after dividing it by 1000000007 (109 + 7).

Input

The first line contains integer t (1 ≤ t ≤ 2·105) — the number of the test data.

Each of the next t lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000).

Output

For each test from the input print the answer to the problem modulo 1000000007 (109 + 7). Print the answers to the tests in the order in which the tests are given in the input.

Examples

Input

6
1 1
2 1
2 2
3 1
3 2
3 3


Output

1
3
0
6
2
0

Note

In the first test sample there is exactly one beautiful sequence: (1, 1).

In the second test sample, the following sequences are beautiful: 

  * (1, 1); 
  * (1, 2); 
  * (2, 2). 



In the fourth test sample, the following sequences are beautiful: 

  * (1, 1); 
  * (1, 2); 
  * (1, 3); 
  * (2, 2); 
  * (2, 3); 
  * (3, 3). 



In the fifth test sample, the following sequences are beautiful: 

  * (1, 1), (2, 3); 
  * (1, 2), (3, 3). 



In the third and sixth samples, there are no beautiful sequences.

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optime(3)
#pragma GCC optime(2)
#pragma GCC optime(1)
using namespace std;
long long n, k, t;
long long ans, a[1001], b[1001][1001], dp[1001][1001];
const long long mod = 1e9 + 7;
signed main() {
  for (register long long i = 0; i <= 1000; ++i) {
    b[i][0] = 1;
    for (register long long j = 1; j <= i; ++j)
      b[i][j] = (b[i - 1][j] + b[i - 1][j - 1]) % mod;
  }
  dp[1][1] = 1;
  a[0] = 1;
  for (register long long i = 1; i <= 1000; ++i) {
    a[i] = a[i - 1] * i % mod;
    for (register long long j = 1; j <= i; ++j) {
      if (i + j < 1001) dp[i + j][j] = (dp[i + j][j] + dp[i][j]) % mod;
      if (i + j < 1000)
        dp[i + j + 1][j + 1] = (dp[i + j + 1][j + 1] + dp[i][j]) % mod;
    }
  }
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d", &n, &k);
    ans = 0;
    for (register long long i = k; i <= n; ++i)
      ans = (ans + dp[i][k] * b[n - i + k][k] % mod * a[k]) % mod;
    printf("%d\n", ans);
  }
  return 0;
}

```