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:
xs = list(map(int, input().split(" ")))

b = bin(xs[0])[2:]
k = xs[1]
r = b.count('1')

ks = []

for i, q in enumerate(reversed(list(b))):
    if q == '1':
        ks.append(i)

if k < len(ks):
    print("NO")
else:
    stack = ks
    ans = []
    p = 0
    q = len(ks)
    while q < xs[1] and len(stack) > 0:
        x = stack.pop()
        if x == 0:
            ans.append(0)
        else:
            stack.append(x - 1)
            stack.append(x - 1)
            q += 1
    if q != k:
        print("NO")
    else:
        ans = ans + stack
        ans = " ".join(list(map(lambda x: str(2 ** x), ans)))
        print("YES")
        print(ans)