Really Good Compression

Time limit1sMemory limit128 MB

Summary

Given N distinct 1000-bit files, decide whether each can be compressed to at most b bits.

Level: Easy3 of 10
Topics: Math, Combinatorics, Bit manipulation, Implementation
Solved: No attempts yet

Problem

When exam season arrives, many people start doing things they normally never do. This exam season, Sanggeun came up with a fantastic compression algorithm.

Using Sanggeun's algorithm, when you compress $N$ files, each file becomes at most $b$ bits after compression. It is hard to believe such a compression algorithm could exist, so write a program that decides whether such an algorithm is theoretically possible.

There are $N$ files to compress, all distinct, and each file consists of $1000$ bits. In other words, no two files are exactly the same.

Input

The first line contains $N$ and $b$ , separated by a space. ( $1 \le N \le 10^{15}$ , $0 \le b \le 50$ )

Output

Print yes if all $N$ files can be compressed so that each file is at most $b$ bits long, and no otherwise.

Examples3

Example 1
Input
```
13 3
```
Expected output
```
yes
```
Example 2
Input
```
1 0
```
Expected output
```
yes
```
Example 3
Input
```
31415926535897 40
```
Expected output
```
no
```