#include <bits/stdc++.h>
using namespace std;
const int maxn = 1000 + 100;
const int maxk = 45;
const int mod = 1000000007;
int dp[maxk][maxn];
int cnt[maxk][maxn];
void input_output() {
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    cin >> n >> k;
    if (k < maxk)
      cout << dp[k][n] << endl;
    else
      cout << 0 << endl;
  }
}
void dpp() {
  for (int i = 0; i < maxn; i++) dp[0][i] = 1, cnt[0][i] = i + 1;
  for (int i = 1; i < 45; i++) {
    for (int j = i; j < maxn; j++) {
      dp[i][j] = (dp[i][j - i] + (long long)i * cnt[i - 1][j - i]) % mod;
      cnt[i][j] = (cnt[i][j - 1] + dp[i][j]) % mod;
    }
  }
}
int main() {
  dpp();
  input_output();
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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>
using namespace std;
const int maxn = 1000 + 100;
const int maxk = 45;
const int mod = 1000000007;
int dp[maxk][maxn];
int cnt[maxk][maxn];
void input_output() {
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    cin >> n >> k;
    if (k < maxk)
      cout << dp[k][n] << endl;
    else
      cout << 0 << endl;
  }
}
void dpp() {
  for (int i = 0; i < maxn; i++) dp[0][i] = 1, cnt[0][i] = i + 1;
  for (int i = 1; i < 45; i++) {
    for (int j = i; j < maxn; j++) {
      dp[i][j] = (dp[i][j - i] + (long long)i * cnt[i - 1][j - i]) % mod;
      cnt[i][j] = (cnt[i][j - 1] + dp[i][j]) % mod;
    }
  }
}
int main() {
  dpp();
  input_output();
}

```