Fill the Grid
Time Limit: 1 Second Memory Limit: 32768 KB
Given an m*n grid, you're required to fill it with the numbers from 1 to m*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*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.
Sample Input
2 3 0 0
Sample Output
5Submit
Source: ZOJ Monthly, November 2004