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 PYTHON3):

Solution:
n,k=map(int,input().split(' '))
a=bin(n)[::-1]
st=[]
import collections
m=collections.Counter(str(a))['1']
if k>n or k<m:
    print('NO')
    import sys
    sys.exit()
else:
    print('YES')
for u in range(0,len(a)-2):
    if a[u]=='0':
        continue
    else:
        st.append(2**u)
while len(st)!=k:
    for i in range(0,len(st)):
        if st[i]>1:
            st[i]=st[i]//2
            st.append(st[i])
        if len(st)==k:
            break
print(*st)