human
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 ≤ x, y ≤ 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.
 ... What is a Python code to find out whether x can be turned into y after a certain number of operations (possibly zero)?
assistant
#Here is Python code to find out whether x can be turned into y after a certain number of operations (possibly zero).

from collections import deque, defaultdict, Counter, OrderedDict
import math,os,sys,heapq,bisect,random
from itertools import *
from io import BytesIO, IOBase
def inp(): return sys.stdin.readline().rstrip("\r\n")  # for fast input
def out(var): sys.stdout.write(str(var))  # for fast output, always take string
def lis(): return list(map(int, inp().split()))
def stringlis(): return list(map(str, inp().split()))
def sep(): return map(int, inp().split())
def strsep(): return map(str, inp().split())
def fsep(): return map(float, inp().split())
def inpu(): return int(inp())
M = 1000000007

def main():
    how_much_noob_I_am = 1
    #how_much_noob_I_am = inpu()
    for _ in range(how_much_noob_I_am):
        x,y = sep()
        q = deque()
        q.append(x)
        visited = set()
        ans = 0
        while(q):
            s = q.popleft()
            ans+=1
            if s==y:
                print("YES")
                exit()
            p = bin(s).replace("0b","")+"0"
            p = p[::-1]
            if p not in visited:
                q.append(int(p,2))
                visited.add(p)
            p = bin(s).replace("0b","")+"1"
            p = p[::-1]
            if p not in visited:
                q.append(int(p,2))
                visited.add(p)
            if ans==10**4:
                break
        print("NO")
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
    def readline(self):
        while self.newlines == 0:
            b =...