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