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().strip().split())

a = []
newN = n
while(newN):
    a.append(newN % 2)
    newN = newN // 2
index = []
count = [0]*len(a)
for i in range(len(a)):
    if a[i] == 1:
        index.append(i)
        count[i] += 1
m = len(index)
ans = []
if m > k or n < k:
    print("NO")
else:
    print("YES")
    if m == k:
        for i in range(m):
            ans.append(2**index[i])
    if m < k:
        i = len(a)-1
        cnt = sum(count)
        while sum(count) < k:
            if i == 0:
                i = len(a)-1
            while count[i] > 0:
                tmp = 2**(i-1)
                count[i] -= 1
                count[i-1] += 2
                cnt += 1
                if k == sum(count):
                    break
            i -= 1
        for i in range(len(count)):
            if count[i]:
                ans.extend([2**i]*count[i])

    print(' '.join(map(str,ans)))