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())
h= [int(_) for _ in (bin(n)[2:])]
plz = list(reversed(h))
options = []
i = 0
for char in range(len(plz)):
    if plz[char] == 1:
        options.append(2 ** char)
if len(options) > k:
    print("NO")
else:
    while len(options) < k:
        try:
            if options[i] != 1:
                half = options[i]/2
                del options[i]
                options.append(half)
                options.append(half)
            else:
                i+=1
        except IndexError:
            print("NO")
            break
    if len(options) == k:
        print("YES")
        printable = list(map(str, map(int, options)))
        print(" ".join(printable))