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())
n = bin(n)
n = n[2:]
l = len(n) - 1
Ans = ""
i = l
comb = []

while i >= 0:
    if n[i] != "0":
        comb.append(2 ** (l - i))
    i -= 1

if len(comb) < k:
    i = len(comb) - 1
    while i >= 0 and len(comb) < k:
        if comb[i] // 2 != 0:
            num = comb.pop(i) // 2
            comb.append(num)
            comb.append(num)
            i = len(comb) - 1
        else:
            i -= 1

if len(comb) == k:
    print("YES")
    for res in comb:
        Ans += str(res) + " "
    print(Ans)
else:
    print("NO")