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())
def binary(n):
    l = []
    while(n>0):
        l.append(n%2)
        n = n//2
    return l
s = 0
t = 0
l = binary(n)
for i in range(len(l)):
    if l[i]:
        s += 2**i
        t += 1
if s>=k and t<=k:
    print("YES")
    i = len(l)-1
    while(t!=k):
        if (t+l[i])<=k:
            t += l[i]
            l[i-1] += 2*l[i]
            l[i] = 0
        else:
            temp = k - t
            l[i] -= temp
            l[i-1] += 2*temp
            t += temp
        i -= 1
    for i in range(len(l)):
        if l[i]:
            print((str(2**i)+" ")*l[i], end = "")
else:
    print("NO")