Problem

You are given a rectangular board of size N × M.

You have an unlimited number of dominoes of size 2 × 1. A domino may be placed either horizontally or vertically.

Determine the number of distinct ways to completely tile the board so that:

• Every cell is covered exactly once.
• Dominoes do not overlap.
• Dominoes remain inside the board.

Since the answer may be very large, print it modulo 10^9 + 7.

Input

N M

Output

Print the number of valid tilings modulo 10^9 + 7.