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

Example Output

6