Confusion

Consider a sequence of length N in which each integer from 1 to N appears exactly once.

A pair of positions is called a confused pair if the earlier number in the sequence is greater than the later number. The confusion degree of a sequence is the number of confused pairs.

For example, the sequence (1, 4, 3, 2) has confusion degree 3, because its confused pairs are (4, 3), (4, 2), and (3, 2).

Given N and C, count the number of length N sequences whose confusion degree is exactly C.

The first line contains two integers N and C.

• 1 <= N <= 1000
• 0 <= C <= 10000

Print the number of length N sequences with confusion degree C, modulo 1,000,000,007.