2017 Winter Waterloo Local ACM Contest, Problem D

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[0]
  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 ~P_1, P_2, \dots, P_N~, 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 ~10^9 + 7~.

Constraints

• ~1 \le N \le 30~
• ~1 \le K \le 900~
• ~N,K~ are integers

Input Specification

The input will be in the format:

~N~ ~K~

Output Specification

Output one integer, the number of possible permutations, modulo ~10^9+7~.

Sample Input 1

3 5

Sample Output 1

2

Explanation of Sample Output 1

The 2 valid permutations are ~2, 1, 3~ and ~2, 3, 1~.

Sample Input 2

5 29

Sample Output 2

0

Sample Input 3

20 100

Sample Output 3

262859528