Beautiful Pairs of Numbers

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.

inputFormat

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).

outputFormat

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.

样例

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

1
3
0
6
2
0

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