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:
try:
    n, k = map(int, input().split())
except:
    exit()
 
if n < k:
    print("NO")
    exit(0)

q = []
s = {}
i = 1
while n:
    if n & 1 != 0:
        if i > 1: q.append(i)
        if i not in s.keys():
            s[i] = 0
        s[i] += 1
    i = i << 1
    n = n >> 1
if len(s) > k:
    print("NO")
    exit(0)

# break down
i = len(s)
while i < k and q:
    top = q.pop(0)
    s[top] -= 1
    if top // 2 not in s.keys():
        s[top // 2] = 0
    s[top // 2] += 2
    if top // 2 > 1:
        q.append(top // 2)
        q.append(top // 2)
    i += 1

if i < k:
    print("NO")
    exit(0)
print("YES", *[k for k in s.keys() for i in range(s[k])])