Chunbae's Special Heart

Interview

Time limit1sMemory limit1024 MB

Summary

Given N and M, decide whether repeatedly splitting a heart into floor and ceiling halves and keeping one half can end at exactly M grams.

Level: Medium5 of 10
Topics: Divide and conquer, Recursion, Math
Solved: No attempts yet

문제

Chunbae has one heart that weighs $N$ g. The kind Chunbae wants to split this heart and give a heart weighing $M$ g to Nabi as a gift!

Chunbae can split his $A$ g heart into 2 hearts. If $A$ is even, it splits into two hearts of $\frac{A}{2}$ g each. If $A$ is odd, it splits into one heart of $\frac{A-1}{2}$ g and one heart of $(\frac{A-1}{2}+1)$ g. Then Chunbae must choose one of the two hearts and discard it. He repeats this process until the one heart he keeps weighs $M$ g. However, once a heart weighs $1$ g, Chunbae cannot split it any further.

Before he splits his heart, Chunbae wants to know whether he can end up with a heart weighing $M$ g. Help him find out.

입력

The first line contains the weight $N$ of Chunbae's heart and the weight $M$ of the heart to give to Nabi, separated by a space. $(1 \le M \le N \le 10^{18}$ , $N$ and $M$ are positive integers $)$

출력

If Chunbae can make a heart weighing $M$ g, print YES. Otherwise, print NO.

Examples2

Example 1
Input
```
13 4
```
Expected output
```
YES
```
Example 2
Input
```
13 5
```
Expected output
```
NO
```