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:
params = list(map(int,list(input().split())))
n = params[0]
size = params[1]

seq = list(map(int,list(bin(n)[2:])))

u = 0
z = 0

for s in seq:
    if s == 1:
        u += 1
    else:
        z += 1

if size < u or size > n:
    print('NO')
else:
    print('YES')
    r = u
    while r in range(u,size):
        
        if seq[0] == 0:
            seq.pop(0)
        seq[0] -= 1
        seq[1] += 2
        r += 1
        
    ans = ''
    for r in range(0, len(seq)):
        ans += (str(2**(len(seq)-r-1)) + ' ') * seq[r]
        
    print (ans[:-1])