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:
import sys
n, k = map(int, input().split())
a = [1 for i in range(k)]
j = 1
s1 = []
x = 1
while True:
    s1.append(x)
    x = 2**j
    if x > n:
        break
    j += 1
for i in range(len(a)):
    for j in range(len(s1)):
        a[i] = s1[j]
        #print(i, a, sum(a))
        if sum(a) == n:
            print('YES')
            for i in a:
                print(i, end=' ')
            sys.exit()
        elif sum(a) > n:
            a[i] = s1[j-1]
            break
print("NO")