시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 256 MB111100.000%

## 문제

Vera is very smart and invented a new sorting algorithm. She coded the following Python function to count how many steps her algorithm takes.

def steps(array):
if len(array) == 0:
return 0
pivot = array
count = 0
lesser = []
greater = []
for element in array: ## looks at each element in the array
count += 1
if element < pivot:
lesser.append(element) ## e.g. [1,3].append(5) => [1,3,5]
elif element > pivot:
greater.append(element)
return count + steps(lesser) + steps(greater)

A permutation P is an ordered set of integers P1, P2, · · · , PN , consisting of N distinct positive integers, each of which are at most N. We will call the number N the size of the permutation.

You are given integers N and K.

Help Vera count the number of permutations P of size N such that steps(P) returns the value K. This number could be large, so output it modulo 109 + 7.

## 입력

The input will be in the format:

N K

Constraints:

• 1 ≤ N ≤ 30
• 1 ≤ K ≤ 900
• N, K are integers

## 출력

Output one integer, the number of possible permutations, modulo 109 + 7.

## 예제 입력 1

3 5


## 예제 출력 1

2


## 예제 입력 2

5 29


## 예제 출력 2

0


## 예제 입력 3

20 100


## 예제 출력 3

262859528


## 힌트

For the first example, the 2 valid permutations are 2, 1, 3 and 2, 3, 1.