human
Write me a Python program to print NO given the following:
A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input

9 4

Output

YES
1 2 2 4 

Input

8 1

Output

YES
8 

Input

5 1

Output

NO

Input

3 7

Output

NO
Using python3 can you solve the prior task?
assistant
#Here is Python program to print NO.

# Author : nitish420 --------------------------------------------------------------------
import os
import sys
from io import BytesIO, IOBase
# mod=10**9+7
# sys.setrecursionlimit(10**6)
# from functools import lru_cache


def main():
    n,k=map(int,input().split())
    s=bin(n)
    ones=s[2:].count("1")
    if k<ones:
        print("NO")
        exit()
    if k>n:
        print("NO")
        exit()
    
    if k==n:
        print("YES")
        print("1 "*(n))
        exit()

    arr=[0]*(31)

    for i in range(31):
        if n & (1<<i):
            arr[i]+=1
    
    sm=sum(arr)

    r=30
    while k!=sm and r>0:
        if arr[r]!=0:
            sm+=1
            arr[r]-=1
            arr[r-1]+=2
        else:
            r-=1

    if k==sm:
        print("YES")
    else:
        print("NO")
        exit()
    
    for i in range(31):
        if arr[i]!=0:
            print(f'{pow(2,i)} '*arr[i],end="")
    print()


    


# region fastio

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 = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b'\n') + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd,...