403764: GYM101262 D Vera and Sorting

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:
    count += 1
    if element < pivot:
      lesser.append(element)
    elif element > pivot:
      greater.append(element)
  return count + steps(lesser) + steps(greater)

A permutation P is an ordered set of integers P₁, P₂, ..., P_N, consisting of N distinct positive integers, each of them doesn't exceed N. We'll call number N the size or the length of permutation.

You are given integers N and K.

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

Constraints:

1 ≤ N ≤ 30

1 ≤ K ≤ 900

N, K are integers

The input will be in the format:

N K

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

3 5

2

5 29

0

20 100

262859528

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