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 math
n,k=[int(x) for x in input().split()]
s=k
arr= [1 for i in range(k)]
i = k - 1
while(i >= 0):
    while (s+ arr[i] <= n): 
        s += arr[i]
        arr[i] *= 2
    i -= 1
if (s != n):
    print("NO") 
else:
    print("YES")
    for i in range(0, k, 1):
        print(arr[i], end = ' ') 


'''n=int(input())
s=input()
i=0
j=1
ans=""
while(i<len(s)):
    ans+=s[i]
    j+=1
    i+=j
print(ans)'''

'''n=int(input())
arr=[int(x) for x in input().split()]
m=max(arr)
i=arr.index(m)
del(arr[i])
m=max(arr)
min_=min(arr)
print(m-min_)'''