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:
from collections import defaultdict
N, K = map(int, input().split())
num = 0
M = N
pow2 = [2 ** i for i in range(31)]
rec = defaultdict(int)
for j in range(min(K + 1, M)):
    for i in range(30, -1, -1):
        if M >= pow2[i]:
            M -= pow2[i]
            num += 1
            rec[i] = 1

if num > K:
    print("NO")
elif num == K:
    print("YES")
    print(" ".join(map(lambda i: str(pow2[i]), rec.keys())))
else:
    for i in range(30, 0, -1):
        while rec[i] > 0:
            if num == K:
                break
            rec[i] -= 1
            rec[i - 1] += 2
            num += 1
    if num < K:
        print("NO")
        exit()
    ans = []
    for i, k in rec.items():
        for j in range(k):
            ans.append(i)

    print("YES")
    print(" ".join(map(lambda i: str(pow2[i]), ans)))