D. Beautiful Pairs of Numbers
combinatorics; dp
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).
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).
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.
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.