Problem: 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

Solution (in PYTHON):

Solution:
#!/usr/bin/python2

import sys
from heapq import *
from collections import Counter

def ir(): return int(raw_input())
def ia(): return map(int, raw_input().split())

n, k = ia()

def pp(n):
    return ((n & (n - 1)) == 0) and n != 0

def dfs0(n, m, k):
    a = dfs(n - m, m, k - 1)
    if a != False:
        return [m] + a
    b = dfs(n, m//2, k)
    if b != False:
        return b
    else:
        return False

D = { }
def dfs(n, m, k):
    if (n, m, k) in D:
        return D[ (n, m, k) ]
    if n == 0 and k == 0:
        return []
    elif n == k:
        return [1] * k
    elif n == 2*k:
        return [2] * k
    elif n == 4*k:
        return [4] * k
    elif n > k * m:
        return False
    elif n > 0 and k == 1 and pp(n):
        return [n]
    elif n > 0 and k == 1:
        return False
    elif n < 0:
        return False
    elif n >= 0 and k == 0:
        return False
    elif n >= 0 and m < 1:
        return False
    elif n < k:
        return False
    else:
        ans = dfs0(n, m, k)
        D[ (n, m, k) ] = ans
        return ans

ans = dfs(n, m = pow(2, 30), k = k)

if ans != False:
    print "YES"
    print " ".join(map(str, ans))
else:
    print "NO"