COCI 2006/2007, Contest #4

Task ZBRKA

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 (1, 4, 3, 2) is 3 because there are 3 confused pairs: (4, 3), (4, 2) and (3, 2).

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

Input

The first and only line of input contains two integers, N (1 ≤ N ≤ 1000) and C (0 ≤ C ≤ 10 000).

Output

Output the number of sequences modulo 1 000 000 007.

Sample Tests

10 1

9

4 3

6

9 13

17957

All Submissions
Best Solutions

Point Value: 15 (partial)
Time Limit: 1.00s
Memory Limit: 64M
Added: Jan 29, 2009

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

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