2552 - Zju2253 Fill the Grid

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.

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.

Examples

Input

2 3
0 0

Output

5

Hint

本题为多组数据,请做到"0 0"结束

Time Limit 1 second
Memory Limit 128 MB
Discuss Stats
上一题 下一题