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:
from collections import deque
n, k = [int(x) for x in input().split()]
q = deque()
cnt = {}
for i in range(30):
    if i > n:
        break
    if n & (1<<i):
        if i > 0:
            q.append(1 << i)
        if 1 << i in cnt:
            cnt[1 << i] +=1
        else:
            cnt[1 << i] = 1
cntLen = len(cnt)
if cntLen > k:
    print("NO")
else:
    while cntLen < k and len(q) > 0:
        z = q.__getitem__(0)
        q.popleft()
        cnt[z] -= 1
        if z/2 in cnt:
            cnt[z/2] += 2
        else:
            cnt[z/2] = 2
        if z/2 > 1:
            q.append(z/2)
            q.append(z/2)
        cntLen += 1
    if cntLen < k:
        print("NO")
    else:
        print("YES")

        for k,v in cnt.items():
            for i in range(v):
                print(int(k),end=" ")