Consider a sequence of \(N\) integers where each integer between \(1\) and \(N\) appears exactly once.

A pair of numbers in the sequence is confused if the number that comes earlier in the sequence is larger than the later number.

The confusion of the sequence is the number of confused pairs in it. For example, the confusion of the sequence \(3\ 2\ 1\) is \(3\) because there are \(3\) confused pairs: \((3, 2)\), \((3, 1)\) and \((2, 1)\).

Write a program that calculates the number of sequences of length \(N\) whose confusion is exactly \(C\).

The first and only line of input contains two integers, \(N\) (\(1 \le N \le 1000\)) and \(C\) (\(0 \le C \le 1000000000\)).

Output the number of sequences modulo \(1000000000\).

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출처 COCI 2006/2007 Contest 4