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.
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 one line for each case. For the answer may be quite huge, you need to output the answer
module 1,000,000,007.
3 0 3 1
1 4
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}
Migrated from old NTUJ.
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