Diplomas

Diana has a collection of certificates from competitions in computer science and local history.

The computer science certificates measure 2×1, with a height of 2 and a width of 1. These certificates are not meant to be rotated. The local history certificates measure 1×3, with a height of 1 and a width of 3, and they also remain unrotated.

Diana's room has a wall with dimensions H×W. Your task is to determine the number of different ways this wall can be completely covered with the certificates, ensuring there is no overlap.

Input

The input consists of two integers H and W, each not exceeding 10.

Output

Output the total number of ways to cover the wall with the certificates.

Examples