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())
b=len(bin(n)[2:])
b1=bin(n)[2:]
if k<b1.count('1') or k>n:
    print('NO')
    exit()
cand=[]
print('YES')
for i in range(b):
    if b1[i]=='1':
        cand.append(2**(b-i-1))
#print(cand)
cand.sort(reverse=True)
diff=(k-b1.count('1'))
while diff:
    for i in range(len(cand)):
        if cand[i]==1:
            continue 
        else:
            if diff==0:
                continue 
            r=cand[i]//2 
            cand.pop(i)
            cand.append(r)
            cand.append(r)
            diff-=1 
print(*cand)