Iterated Sums

The function $S$ is defined as follows.

• $S(0, n) = n$ for every positive integer $n$
• $S(k, n) = S(k-1, 1) + S(k-1, 2) + \dots + S(k-1, n)$ for all positive integers $k$ and $n$

In other words, $S(k, n)$ adds up the values of the function one level below, from $1$ through $n$.

Given $k$ and $n$, write a program that computes $S(k, n)$ modulo 1,000,000,007.

The first line contains $k$ and $n$, separated by a space. ($1 \le k \le 50$, $1 \le n \le 1{,}000{,}000{,}000$)

Print $S(k, n)$ modulo 1,000,000,007 on the first line.