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:
ina = input().split()
n = int(ina[0])
k = int(ina[1])
n1 = n
ans = 0
c = []
s = 1
while (n > 0):
    if (n & 1):
        ans += 1
        c.append(s)
    s *= 2
    n = n >> 1
if (ans <= k and k <= n1):
    print("YES")
    t = 0
    while (len(c) < k):
        if (c[t] > 1):
            c.append(c[t] // 2)
            c[t] = c[t] // 2
        else:
            t+= 1
    for i in c:
        print(i, end=' ')
else:
    print("NO")