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 Counter
n, k = list(map(int, input().split()))
s = bin(n)[2:]
c = Counter(s)
if k > n or c['1'] > k:
    print('NO')
else:
    print('YES')
    c = Counter()
    i = 1
    t = 0
    for e in reversed(s):
        if e == '1':
            c[i] += 1
            t += 1
        i *= 2
    max_i = i
    while t < k:
        if c[i] == 0:
            i //= 2
            continue
        if c[i] + t <= k:
            c[i // 2] += c[i] * 2
            t += c[i]
            c[i] = 0
            i //= 2
        else:
            c[i // 2] += (k - t) * 2
            c[i] -= (k - t)
            break
    i = 1
    r = []
    while i <= max_i:
        if c[i] > 0:
            r += [i] * c[i]
        i *= 2
    print(' '.join(map(str, r)))