A game of digits

Consider the following game: given two positive integers n and b,
players A and B take turns to write digits in base b (from 0 to b − 1),
starting with player A. The digits are written from left to right. For
instance, if A writes a 5, B may write a 1 to form a 51, but not a 15.
(And then A would write another digit, and then B, and so on.) If at any
point during the game a multiple of n (including 0) is written (in base
b), then B wins and the game finishes.

If A can indefinitely prevent B from winning, both players will
eventually get bored and player A will be declared the winner.
Otherwise, they will keep playing until B wins. Can you determine who
will be the winner? Assume that A and B play perfectly.

Input

Input consists of several cases, each with n and b. Assume 1 ≤ n ≤ 10¹⁸
and 2 ≤ b ≤ 10¹⁸.

Output

For every case, print the name of the winner.

Problem information

Author: Martí Oller

Generation: 2026-01-25T11:37:50.095Z

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