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 = tuple(map(int, input().split()))

b = bin(n)[2:]
count = 0

d = dict()

for i in range(1, len(b) + 1):
    if b[-i] == '1':
        d[i - 1] = 1
        count += 1

for i in range(max(d.keys()) - 1, -1, -1):
    if i not in d.keys():
        d[i] = 0

if k > n or k < count:
    print('NO')
else:
    print('YES')
    
    for i in range(k - count):
        max_key = max(d.keys())
        
        d[max_key] = d[max_key] - 1
        d[max_key - 1] = d[max_key - 1] + 2
        
        if d[max_key] == 0:
            d.pop(max_key)
    
    A = list(d.items())
    
    for item in A:
        for i in range(item[1]):
            print(2 ** item[0], end=' ')