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())
a = list(map(int, list(str(bin(n)).lstrip('0b'))))
c = a.count(1)
j = 0
while c < k:
    if j > len(a) - 2:
        break
    if a[j]:
        c += 1
        a[j] -= 1
        a[j + 1] += 2
    else:
        j += 1
if c != k:
    print('NO')
else:
    print('YES')
    for i in range(len(a)):
        for k in range(a[i]):
            print(2 ** (len(a) - i - 1), end=' ')