# Problem 325: Stone Game II
A game is played with two piles of stones and two players. At her turn,
a player removes a number of stones from the larger pile. The number of
stones she removes must be a positive multiple of the number of stones
in the smaller pile. E.g., let the ordered pair(6,14) describe a
configuration with 6 stones in the smaller pile and 14 stones in the
larger pile, then the first player can remove 6 or 12 stones from the
larger pile. The player taking all the stones from a pile wins the game.
A winning configuration is one where the first player can force a win.
For example, (1,5), (2,6) and (3,12) are winning configurations because
the first player can immediately remove all stones in the second pile. A
losing configuration is one where the second player can force a win, no
matter what the first player does. For example, (2,3) and (3,4) are
losing configurations: any legal move leaves a winning configuration for
the second player. Define S(N) as the sum of (xi+yi) for all losing
configurations (xi,yi), 0 < xi < yi ≤ N. We can verify that S(10)
= 211 and S(104) = 230312207313. Find S(1016) mod 710.