Vera and Sorting

Vera invented a new sorting algorithm. She wrote the Python function below 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 $P$ of size $N$ is an ordered sequence of integers $P_1, P_2, \dots, P_N$ whose $N$ entries are distinct positive integers, each of them at most $N$.

You are given integers $N$ and $K$. Count the permutations $P$ of size $N$ for which $steps(P)$ returns $K$. The count can be large, so print it modulo $10^9 + 7$.

The first line contains two integers $N$ and $K$ separated by a space.

• $1 \le N \le 30$
• $1 \le K \le 900$

Print the number of such permutations modulo $10^9 + 7$ on a single line.

For $N = 3$ and $K = 5$ the two valid permutations are $(2, 1, 3)$ and $(2, 3, 1)$.