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Little Elephant from the Zoo of Lviv likes permutations.
A permutation of size N is a sequence (a_{1}, ..., a_{N}) that contains each of the numbers from 1 to N exactly once.
For example, (3,1,4,5,2) is a permutation of size 5.
Given two permutations A = (a_{1}, ..., a_{N}) and B = (b_{1}, ..., b_{N}), the value magic(A,B) is defined as follows:
magic(A,B) = max(a_{1},b_{1}) + max(a_{2},b_{2}) + ... + max(a_{N},b_{N}).
You are given the int N.
You are also given another int K.
Let X be the number of pairs (A,B) such that both A and B are permutations of size N, and magic(A,B) is greater than or equal to K.
(Note that A and B are not required to be distinct.) Return the value (X modulo 1,000,000,007).
