### 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

## Input10 1 ## Output9 |
## Input4 3 ## Output6 |
## Input9 13 ## Output17957 |

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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