The sequence of integer pairs (a 1, b 1), (a 2, b 2), ..., (a k , b k ) is beautiful, if the following statements are fulfilled: 1 ≤ a 1 ≤ b 1 a 2 ≤ b 2 a k ≤ b k ≤ n , where n is a given positive integer; all numbers b 1 - a 1 , b 2 - a 2 , ..., b k - a k 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).
输入描述:
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).
输出描述:
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.
示例1
输入
6<br />1 1<br />2 1<br />2 2<br />3 1<br />3 2<br />3 3<br />
输出
1<br />3<br />0<br />6<br />2<br />0<br />
备注:
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.
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