Problem Description

Given an $m\times n$ grid, you're required to fill it with the numbers from $1$ to $m\times n$ 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 $2\times 3$ grid, we have the following solutions:

456  356  256  246  346
123  124  134  135  125

Thus, the sum is $5$.

Input Format

Two positive integer $m, n$ per line. Two zeros indicate the end of input.

Output Format

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

Sample

2 3
0 0

5

Data scope and agreement

For data of $100 \%$: $0<m, n<10$.

This question involves multiple sets of data, please complete with 0 0.