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 = map(int, input().split())
if k > n:
    print('NO')
    exit()

nb = bin(n)[-1:1:-1]
ans = {}
c = 0
for i in range(len(nb)):
    if nb[i] == '1':
        if nb[i] not in ans:
            ans[2**i] = 1
        else:
            ans[2**i] += 1
        c += 1
#print(ans)
if k < c:
    print('NO')
    exit()

while c != k:
    for i, j in ans.items():
        if i != 1 and j != 0:
            ans[i] -= 1
            if i//2 not in ans:
                ans[i//2] = 2
            else:
                ans[i//2] += 2
            break
    c += 1
print('YES')
for k,v in ans.items():
    for _ in range(v):
        print(k, end=' ')