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 = list(map(int,input().split(' ')))
s = ""
r = n[0]
k = n[0]
z = n[1]
a = []
b = 0
while k != 0:
    if k%2 == 0:
        s += "0"
    else:
        s += "1"
        a += [2**b]
    b += 1
    k = k//2
if len(a) > z or z > r:
    print("NO")
else:
    c = 0
    print("YES")
    while len(a) < z:
        if a[c] != 1:
            a.append(a[c]//2)
            a[c] = a[c]//2
        else:
            c += 1
    for i in a:
        print(i)