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:
entrada = input().split()
n = int(entrada[0])
k = int(entrada[1])

arr_result = []
k_temp = k
n_temp = n
soma = 0
m = 0

i = 30
while i >= 0 and k >= 0:
    m = 1 << i
    if (m > n) or (n - m < k - 1):
        i -= 1
        continue
    soma += m
    arr_result.append(m)
    n -= m
    k -= 1

if (len(arr_result) == k_temp and soma == n_temp):
    print("YES")

    for resp in arr_result:
        print(resp, end=" ")
    print("")
else:
    print("NO")