The Game of Stars and Roses#1298
The little prince loved counting stars, and the fox, in turn, cherished his roses. The fox invented a game in which both could learn something.
The game is played with a rectangular star map consisting of stars horizontally and stars vertically. The little prince always goes first. In one move, it is allowed to divide the star map—or any of its parts obtained after the first or subsequent moves—into parts. The player who is able, on their move, to get a minimal star of size 1 \times 1 wins and gets all the stars; the loser gets a rose.
If the little prince wins, he joyfully exclaims: "The little prince — the stars!", and the fox, with no less delight, continues: "And the fox gets a rose!". For the fox knew that his rose was unique in all the universe, because he had tamed it. But if the fox wins—neither of them says anything.
Your task is to determine how many times the joyful exclamations of the little prince and the fox will be heard, i.e., the number of games in which both are satisfied with the result, given that they initially play for the stars, not for the rose, and both follow an optimal strategy.
The input contains several test cases, each on a separate line: two integers—the dimensions of the star map and (2 \leq W, H \leq 200). The input ends with a line containing two zeros, which should not be processed.
Output a single number—the number of times the joyful exclamations of the little prince and the fox will be heard.
Example 1