Diplomas#5435

Diplomas

1 second

64 megabytes

Very easy

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

The computer science certificates are of size $2 \times 1$ 2 \times 1, with height $2$ and width $1$ . These certificates cannot be rotated. The local history certificates are of size $1 \times 3$ 1 \times 3, with height $1$ and width $3$ , and they also must not be rotated.

Diana's room has a wall of size $H \times W$ H \times W. Determine the number of different ways the wall can be completely covered with certificates, without any overlap.

Input

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

Output

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

Examples

Example 1

Loading

2 \times 1

1 \times 3

H \times W