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())
b = bin(n)[2:][::-1]
t = b.count('1')

if k < t:
    print('NO')
    exit(0)

s, i = [], 1

for j in b:
    if j == '1':
        s.append(i)
    i *= 2

j = len(s) - 1

ans = []

while k - t > 0:
    if s[j] != 1:
        s[j] //= 2
        s.append(s[j])
        t += 1
        j += 1
    else:
        if j == 0:
            break
        else:
            ans.append(str(s[j]))
            del s[j]
            j -= 1
print('YES\n' + ' '.join(map(str, ans + s)) if len(s) + len(ans) == k else 'NO')