Board Game#7804
Two players play a simple game on a chessboard with dimensions N \times M. The board's rows are numbered from to , and the columns from to . The first player controls a white pawn, which initially occupies the cell (RW, CW). The second player controls a black pawn, starting at (RB, CB). The first player moves first.
On each turn, a player chooses one of four diagonal directions — northeast, northwest, southeast, or southwest — and moves their pawn any positive number of cells in that direction. The game ends when, after a move, both pawns occupy the same cell. The player who moves and causes this overlap is declared the winner.
Both players use optimal strategies: if a player can win, they will minimize the total number of moves; if not, they will maximize the total number of moves. Determine the outcome of the game.
The first line contains two integers and (2 \le N, M \le 10^9).The second line contains four integers , , , (1 \le RW, RB \le N;~1 \le CW, CB \le M) — the initial positions of the white and black pawns. The initial positions (RW, CW) and (RB, CB) are distinct.
If the first player wins, print White (without quotes).If the second player wins, print Black (without quotes).If neither player can win, print Draw (without quotes).Here, is the total number of moves in the game.
Example 1
Example 2
Example 3
In the second example, the first player has two possible moves on the first turn. Moving the white pawn to results in a loss on the following move, so the optimal strategy is to move to . The second player then moves to , after which the first player returns to . The second player can then complete the game on the next move.