#include <bits/stdc++.h>
using namespace std;
int T, N, K;
long long Ans[200005], DP[45][1005], F[1005], Pref[45][1005];
vector<int> Query[45][1005];
int main() {
  cin >> T;
  for (int i = 1; i <= T; i++) {
    cin >> N >> K;
    if (K < 45) Query[K][N].push_back(i);
  }
  F[0] = F[1] = 1;
  for (long long i = 2; i <= 1000; i++) F[i] = (F[i - 1] * i) % 1000000007;
  for (int i = 0; i <= 1000; i++) Pref[0][i] = 1;
  for (int sz = 1; sz <= 1000; sz++)
    for (int i = 44; i > 0; i--)
      for (int j = 1; j <= 1000; j++) {
        if (j >= sz) DP[i][j] += Pref[i - 1][j - sz];
        Pref[i][j] = Pref[i][j - 1] + DP[i][j];
        DP[i][j] %= 1000000007;
        Pref[i][j] %= 1000000007;
        if (sz == 1000)
          for (int q : Query[i][j]) Ans[q] = (Pref[i][j] * F[i]) % 1000000007;
      }
  for (int i = 1; i <= T; i++) cout << Ans[i] << "\n";
}

### Prompt

Please create a solution in CPP 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>
using namespace std;
int T, N, K;
long long Ans[200005], DP[45][1005], F[1005], Pref[45][1005];
vector<int> Query[45][1005];
int main() {
  cin >> T;
  for (int i = 1; i <= T; i++) {
    cin >> N >> K;
    if (K < 45) Query[K][N].push_back(i);
  }
  F[0] = F[1] = 1;
  for (long long i = 2; i <= 1000; i++) F[i] = (F[i - 1] * i) % 1000000007;
  for (int i = 0; i <= 1000; i++) Pref[0][i] = 1;
  for (int sz = 1; sz <= 1000; sz++)
    for (int i = 44; i > 0; i--)
      for (int j = 1; j <= 1000; j++) {
        if (j >= sz) DP[i][j] += Pref[i - 1][j - sz];
        Pref[i][j] = Pref[i][j - 1] + DP[i][j];
        DP[i][j] %= 1000000007;
        Pref[i][j] %= 1000000007;
        if (sz == 1000)
          for (int q : Query[i][j]) Ans[q] = (Pref[i][j] * F[i]) % 1000000007;
      }
  for (int i = 1; i <= T; i++) cout << Ans[i] << "\n";
}

```