yaworsw/euler-manager

---
:id: 325
:name: Stone Game II
:url: https://projecteuler.net/problem=325
:content: |+
  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(<var>N</var>) as the sum of (<var>x</var><sub><var>i</var></sub>+<var>y</var><sub><var>i</var></sub>) for all losing configurations (<var>x</var><sub><var>i</var></sub>,<var>y</var><sub><var>i</var></sub>), 0 \< <var>x</var><sub><var>i</var></sub> \< <var>y</var><sub><var>i</var></sub> ≤ <var>N</var>. We can verify that S(10) = 211 and S(10<sup>4</sup>) = 230312207313.

  Find S(10<sup>16</sup>) mod 7<sup>10</sup>.