Sherry likes matrices a lot, but her favorite ones are humble matrices. An $N\times M$ matrix (we'll call it $\mbox{A}$) is humble if:

It contains all the elements in range $[1,N\times M]$ exactly once.
For any $2$ elements $(i_1,j_1)$ and $(i_2,j_2)$ in matrix $\mbox{A}$:

If $i_{1}+j_{1}<i_{2}+j_{2}$ , then $A_{i_1,j_1}<A_{i_2,j_2}$ should hold.

Given $N$ and $\mbox{M}$, find and print the total number of possible humble matrices; as this number can be quite large, print your answer modulo $10^9+7$.

Input Format

Two space-separated integers, $N$ and $\mbox{M}$, respectively.

Constraints

$1\leq N,M\leq10^{6}$

Scoring

$1\leq N,M\leq10^3$ for $30\%$ of the test data.
$1\leq N,M\leq10^{6}$ for $100\%$ of the test data.

Output Format

Print the total number of humble matrices possible, modulo $10^9+7$.

Sample Input 0

2 2

Sample Output 0

2

Sample Input 1

3 2

Sample Output 1

4

Explanation

There are $2$ possible $2\times2$ humble matrices:

[ 1, 2 ]
[ 3, 4 ]

[ 1, 3 ]
[ 2, 4 ]

Thus, we print the result of $2\%(10^9+7)$, which is $2$.

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