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())
li = {}
tmpn = n
beki = 2**31
s = 0
while beki > 0:
    if tmpn >= beki:
        li[beki] = 1
        tmpn -= beki
        s += 1
    else:
        li[beki] = 0
    beki //= 2

if s > k or n < k:
    print("NO")
    quit()

beki = 2**31
while s != k:
    if li[beki] == 0:
        beki //= 2
    else:
        li[beki] -= 1
        li[beki//2] += 2
        s += 1

print("YES")
ans = []
for i in li:
    for j in range(li[i]):
        ans.append(i)
print(" ".join(map(str,ans)))