F. Reverse
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two positive integers $$$x$$$ and $$$y$$$. You can perform the following operation with $$$x$$$: write it in its binary form without leading zeros, add $$$0$$$ or $$$1$$$ to the right of it, reverse the binary form and turn it into a decimal number which is assigned as the new value of $$$x$$$.

For example:

  • $$$34$$$ can be turned into $$$81$$$ via one operation: the binary form of $$$34$$$ is $$$100010$$$, if you add $$$1$$$, reverse it and remove leading zeros, you will get $$$1010001$$$, which is the binary form of $$$81$$$.
  • $$$34$$$ can be turned into $$$17$$$ via one operation: the binary form of $$$34$$$ is $$$100010$$$, if you add $$$0$$$, reverse it and remove leading zeros, you will get $$$10001$$$, which is the binary form of $$$17$$$.
  • $$$81$$$ can be turned into $$$69$$$ via one operation: the binary form of $$$81$$$ is $$$1010001$$$, if you add $$$0$$$, reverse it and remove leading zeros, you will get $$$1000101$$$, which is the binary form of $$$69$$$.
  • $$$34$$$ can be turned into $$$69$$$ via two operations: first you turn $$$34$$$ into $$$81$$$ and then $$$81$$$ into $$$69$$$.

Your task is to find out whether $$$x$$$ can be turned into $$$y$$$ after a certain number of operations (possibly zero).

Input

The only line of the input contains two integers $$$x$$$ and $$$y$$$ ($$$1 \le x, y \le 10^{18}$$$).

Output

Print YES if you can make $$$x$$$ equal to $$$y$$$ and NO if you can't.

Examples
Input
3 3
Output
YES
Input
7 4
Output
NO
Input
2 8
Output
NO
Input
34 69
Output
YES
Input
8935891487501725 71487131900013807
Output
YES
Note

In the first example, you don't even need to do anything.

The fourth example is described in the statement.