15442번 - Vera and Sorting 다국어

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 P₁, P₂, · · · , 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 10⁹ + 7.

The input will be in the format:

N K

Constraints:

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

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

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