In the ancient game of Lim, two aliens take turns removing sticks from a pile with \(N\) sticks. On each turn, the current player must chose to remove at least \(1\) but no more than \(K\) sticks from the pile. Today, we will play the "misère" variation of Lim, where the last alien to take a stick loses.

Input Specification

The input will contain two space-separated integers \(N\) \((1 \le N \le 10^{18})\) and \(K\) \((1 \le K \le 12)\).

Output Specification

Output YES if the first alien is guaranteed to win if they play perfectly. Otherwise, output NO.

Constraints

Subtask 1 [40%]

\(N \le 30\)

Subtask 2 [40%]

\(N \le 10^6\)

Subtask 3 [20%]

No additional constraints.

Sample Input 1

2 9

Sample Output 1

YES

Explanation for Sample Output 1

The first alien can simply take \(1\) stick and force the second player to take the last.

Sample Input 2

21 3

Sample Output 2

NO