Problem Statement

Royal Game Master Problem Description An exhibition hall runs an annual strategy tournament, and this year two friendly rivals, Player One and Player Two, have designed a brand-new game to test the tournament's sharpest competitors. The game is played on a 1xN board holding K tokens. The tokens come in two colors, white and black, split evenly between the two colors. The white tokens begin in alternating squares starting from the leftmost square, while the black tokens begin in alternating squares ending at the rightmost square. Player One controls every white token, and Player Two controls every black token. Play follows a strict set of rules: White tokens may move only rightward, and black tokens may move only leftward. A single move may shift a token by at most D squares. Tokens can never jump over one another, so careful positioning matters. No token may ever move past either end of the board. Turns alternate between the two players, with Player One moving first. Whoever cannot mak