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:
from collections import deque
n, k = map(int, raw_input().split())
nstr = str(bin(n))[2:]
def decodestr(nstr):
    tmp = []
    nstr = nstr[::-1]
    for idx, c in enumerate(nstr):
        # print(idx, c)
        if c == '1':
            binstr = '0b'+ '1' + '0'*idx
            tmp.append(int(binstr, 2))
    tmp.reverse()
    return tmp

    
tmp = decodestr(nstr)
if (k > n) or (k < len(tmp)):
    print('NO')
    exit(0)
dlist = deque(tmp)
while len(dlist) < k:
    item = dlist.popleft()
    if item == 1:
        dlist.append(item)
    else:
        item = item / 2
        dlist.append(item)
        dlist.append(item)
print('YES')        
print(' '.join([str(i) for i in dlist]))