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(" ")))
n_ = n
ans = []
index = 1
while n != 0:
    if n % 2 == 1:
        ans.append(index)
    index *= 2
    n //= 2
if len(ans) <= k and n_ >= k:
    num_1 = 0
    k_ = len(ans)
    while k_ != k:
        if ans[-1] == 1:
            num_1 += 1
            ans = ans[:-1]
            continue
        last = ans[-1]
        ans = ans[:-1]
        ans.append(last//2)
        ans.append(last//2)
        k_ += 1
    for _ in range(num_1):
        ans.append(1)
    print("YES")
    print(" ".join(map(str, ans)))

else:
    print("NO")