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.

见题面 Input 部分

见题面 Output 部分

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

The fourth example is described in the statement.