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:
import atexit
import io
import sys
from math import *

_INPUT_LINES = sys.stdin.read().splitlines()
raw_input = iter(_INPUT_LINES).next
_OUTPUT_BUFFER = io.BytesIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
    
n,k=map(int,raw_input().split())
b = bin(n)[2:]
# ~ b = b[::-1]
mn = b.count('1')
if k<mn or k>n:
	print 'NO'
	sys.exit(0)
a=[0]*len(b)
for i in range(len(b)):
	if b[i]=='1':
		a[i]=1
# ~ print d
# ~ sys.exit()
diff = k-mn
flag = False
for i in range(len(a)):
	tmp = a[i]
	for j in range(min(diff,tmp)):
		if not diff:
			flag=True
			break
		a[i]-=1
		a[i+1]+=2
		diff-=1
	if flag:
		break
print 'YES'
for i in range(len(a)):
	for j in range(a[i]):
		print 2**(len(a)-1-i),
print