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 = [int(_) for _ in input().split()]
b = [int(_) for _ in bin(n)[2:]]
c = b.count(1)
b.reverse()
z = []
for i in range(len(b)):
    if b[i] == 1:
        z.append(2**(i))

count = 0
ans = ""
if(k == c):
    print("YES\n"+" ".join([str(_) for _ in z]))
elif k < c or k > n:
    print("NO")
else:
    while(len(z)+count < k):
        m = z.pop()
        if(m == 1):
            count += 1
            ans+=" "+str(m)
        else:
            z.append(m//2)
            z.append(m//2)
    for f in z:
        ans += " "+str(f)
    
    print("YES\n" + ans.strip())