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