#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr ll mod = 1e9 + 7;
constexpr int kMaxN = 1003;
ll dp[kMaxN][kMaxN];
ll f[kMaxN];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  f[0] = 1;
  for (int i = 1; i < kMaxN; ++i) {
    dp[i][1] = 1LL * i * (i + 1) / 2;
    f[i] = f[i - 1] * i % mod;
  }
  for (int i = 2; i < kMaxN; ++i) {
    for (int j = 2; j < kMaxN; ++j) {
      dp[i][j] = dp[i - 1][j];
      for (int k = 0; i - j * (k + 1) > 0; ++k) {
        dp[i][j] += dp[i - j * (k + 1)][j - 1];
      }
      dp[i][j] %= mod;
    }
  }
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    cout << dp[n][k] * f[k] % mod << '\n';
  }
  return 0;
}

### Prompt

Develop a solution in CPP 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;
using ll = long long;
constexpr ll mod = 1e9 + 7;
constexpr int kMaxN = 1003;
ll dp[kMaxN][kMaxN];
ll f[kMaxN];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  f[0] = 1;
  for (int i = 1; i < kMaxN; ++i) {
    dp[i][1] = 1LL * i * (i + 1) / 2;
    f[i] = f[i - 1] * i % mod;
  }
  for (int i = 2; i < kMaxN; ++i) {
    for (int j = 2; j < kMaxN; ++j) {
      dp[i][j] = dp[i - 1][j];
      for (int k = 0; i - j * (k + 1) > 0; ++k) {
        dp[i][j] += dp[i - j * (k + 1)][j - 1];
      }
      dp[i][j] %= mod;
    }
  }
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    cout << dp[n][k] * f[k] % mod << '\n';
  }
  return 0;
}

```