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:
def pr(d):
    print('YES')
    for k in d:
        for _ in range(d[k]): print(2**k,end=' ')
n,k = map(int, input().split())
d = {}
for p,v in enumerate(bin(n)[:1:-1]):
    d[p] = int(v)
b = sum(d.values())
i = max(d.keys())
if k>n or k<b: print('NO')
else:
    while b<k:
        if d[i]:
            d[i-1]+=2
            d[i]-=1
            b+=1
        else: i-=1
    pr(d)