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 = list(map(int, input().split()))
ans = []
def myrec(dig):
    a = 1
    if dig == 0:
        return
    while a <= dig:
        a *= 2
    a //= 2
    dig -= a
    ans.append(a)
    myrec(dig)
myrec(n)
ans.sort(reverse=True)
i = 0
while len(ans) < k and i <= len(ans) - 1:
    if ans[i] == 1:
        i += 1
        continue
    ans.append(ans[i] // 2)
    ans[i] = ans[i] // 2
    
if len(ans) != k:
    print('NO')
else:
    print('YES')
    print(' '.join(map(str,ans)))