Given a permutation a1,a2,...aN of {1,2,...,N}, we define its E-value as the amount of elements where ai > i. For example, the E-value of permutation {1, 3, 2, 4} is 1, while the E-value of {4, 3, 2, 1} is 2. You are requested to find how many permutations of {1, 2, . . . , N } whose E-value is exactly k. Input There are several test cases, and one line for each case, which contains two integers, N and k. (1 ≤ N ≤ 1000,0 ≤ k ≤ N). Output Output one line for each case. For the answer may be quite huge, you need to output the answer module 1,000,000,007. Explanation for the sample: There is only one permutation with E-value 0: {1,2,3}, and there are four permutations with E-value 1: {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1} Sample Input 30 31 Sample Output 1 4