A famous NP-complete problem is to detect if a graph can be colored using at most k colors. In a valid coloring, each node is given a color and each edge connects two nodes with different colors.

In this problem, your task is to find out if a cycle graph of n nodes can be colored using at most k colors. A cycle graph consists of a single cycle.

Input

The only input line has two integers n and k.

Output

Print "YES", if the graph can be colored, and "NO" otherwise.

Constraints

• 3 \le n \le 10^9
• 1 \le k \le 10^9

Example

Input:

5 3

Output:

YES