1547: CF832 - A. Sasha and Sticks
[Creator : ]
Description
It's one more school day now. Sasha doesn't like classes and is always bored at them. So, each day he invents some game and plays in it alone or with friends.
Today he invented one simple game to play with Lena, with whom he shares a desk. The rules are simple. Sasha draws $n$ sticks in a row. After that the players take turns crossing out exactly $k$ sticks from left or right in each turn. Sasha moves first, because he is the inventor of the game. If there are less thanksticks on the paper before some turn, the game ends. Sasha wins if he makes strictly more moves than Lena. Sasha wants to know the result of the game before playing, you are to help him.
Input
The first line contains two integers $n,k\ (1≤n,k≤10^{18},\ k≤n)$ − the number of sticks drawn by Sasha and the numberk − the number of sticks to be crossed out on each turn.
Output
If Sasha wins, print
YES, otherwise print NO. Sample 1 Input
1 1
Sample 1 Output
YES
Sasha crosses out 1 stick, and then there are no sticks. So Lena can't make a move, and Sasha wins.
Sample 2 Input
10 4
Sample 2 Output
NO
Sasha crosses out 4 sticks, then Lena crosses out 4 sticks, and after that there are only 2 sticks left. Sasha can't make a move. The players make equal number of moves, so Sasha doesn't win.