Description

Given an mn grid, you're required to fill it with the numbers from 1 to mn but the following rules should be satisfied:

1. each number in grid is larger than its above;
2. each number in grid is larger than its left.

Now, I wonder how many distinct solutions I could make on a grid.

For example. Consider such a 2*3 grid, we have the following solutions:

123  124  134  135  125
		456  356  256  246  346

Thus, the sum is 5.

Format

Input

Two positive integer m, n (0 < m, n < 10) per line. Two zeros indicate the end of input.

Output

A single integer per line for each case -- the number of distinct solutions.

Samples

2 3
0 0

5