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:]
min1 = b.count('1')

if n < k:
    print('NO')
elif min1 > k:
    print('NO')
else:
    print('YES')
    i = 0
    pows = []
    while i < len(b):
        idx = len(b) - 1 - i
        if b[idx] == '1':
            pows.append(2 ** i)
        i += 1
    while len(pows) != k:
        i = len(pows) - 1
        while pows[i] == 1 or pows[i] == 0:
            i -= 1
        while pows[i] != 1 and len(pows) != k:
            pows.append(pows[i] // 2)
            pows[i] //= 2
    ans = ' '.join(map(str, pows))
    print(ans)