1-Pile Nim


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Points: 7 (partial)
Time limit: 2.0s
Memory limit: 32M

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Problem type

You are playing a game with your friend. There is a pile of \(N\) rocks, and you start removing rocks from the pile, then you take turns with your friend. On your turn, you can remove \(1\) to \(K\) rocks from the pile. The person who takes the last rock loses. If you both play optimally, who will win?

Input Specification

The first line will contain the integers \(N, K\) \((1 \le N, K \le 10^9)\).

Output Specification

If you will win, print :hudab:, otherwise print baf.

Constraints

Subtask 1 [80%]

\((1 \le N \le 10^6)\)

Subtask 2 [20%]

No additional constraints.

Sample Input 1

10 3

Sample Output 1

:hudab:

Sample Input 2

15 6

Sample Output 2

baf

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