During his interview, Shil came across a very difficult problem. The problem is as follows:

A matrix V consisting of N rows and M columns is called beautiful if and only if it satisfies the following two conditions:

1) Every cell of the matrix contains distinct natural number less or equal to N*M.
2) For any two cells of the matrix, (i₁,j₁) and (i₂,j₂), if (i₁^j₁) > (i₂^j₂) then v[i₁][j₁] > v[i₂][j₂] .

^ denotes Bitwise XOR operation.

Note that 1 ≤ i₁,i₂ ≤ N and 1 ≤ j₁,j₂ ≤ M.

Given N and M , you have to calculatethe total number of beautiful matrices of size N x M. Since, problem is being very difficult for Shil to solve, he asks for your help.

Input format:
The Input consists of two integers N and M representing the number of rows and columns respectively.

Output format:
Output the total number of Beautiful Matrices of size N x M. Since, this answer can be large, output it modulo 10⁹+7

Constraints:
1 ≤ N,M ≤ 1000