There are $n$ children and $m$ apples that will be distributed to them. Your task is to count the number of ways this can be done.

For example, if $n=3$ and $m=2$, there are $6$ ways: $[0,0,2]$, $[0,1,1]$, $[0,2,0]$, $[1,0,1]$, $[1,1,0]$ and $[2,0,0]$.

Input

The only input line has two integers $n$ and $m$.

Output

Print the number of ways modulo $10^9+7$.

Constraints

• $1 \le n,m \le 10^6$

Example

Input:

3 2

Output:

6