Moving Chips (Large Input)

Alice and Bob are playing a game called Moving Chips. The game is played on an n×mn \times m board where some cells have some chips on it. Two players move alternately. Each turn consists of one person moving a chip to any cell to its left or any cell to its top. For example, the possible movements of chip A on a 3×53\times 5 board is:

The last player who moves all the chips to the top left cell wins.

Consider the configuration of a 100×100100\times 100 board in this file. . denotes an empty cell and a digit denotes the number of chips on that cell.

Alice will move first. Assume that both players move optimally, who will win the game?

Clarifications:​

  • The chips can be stacked on top of each other.
  • Only one chip may be moved at a time (not a stack), but a chip can move any number of spaces in a single direction (left or up).
  • The chips can move passing any chips.
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