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())
st = 1
old_n = n
while st <= n:
    st *= 2
st //= 2
a = list()
while (n > 0):
    if n >= st:
        n -= st
        a.append(st)
    else:
        st //= 2
n = old_n
if len(a) > k:
    print("NO")
elif k > n:
    print("NO")
else:
    i = 0
    while (len(a) < k):
        if a[i] != 1:
            a[i] //= 2
            a.append(a[i])
        else:
            i += 1
    print("YES")
    print(*a)