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:
n , k = input().split(' ')

n = int(n)
k = int(k)

a = []
temp = 1

while(temp <= n):
    
    a.append(temp)
    
    temp = temp*2
    

if k == 1:
    
    found = 0
    
    for i in a:
        if n == i:
            found = 1
            break
        
    if found:
        print("YES")
        print(n)
        
    else:
        print("NO")
   
elif k > n:
    print("NO")
    
elif k == n:
    print("YES")
    for i in range(n):
        print(1, end =" ")  

        
else:
    
    value = n
    temp1 = len(a) - 1
    res = []
    
    temp_sum = 0
    
    while k >0:
        
        temp2 = n - a[temp1]
        if temp2 < k-1:
            temp1 -= 1
        else:
            temp_sum += a[temp1]
            res.append(a[temp1])
            n -= a[temp1]
            k -= 1
            
    if temp_sum != value:
        print("NO")
        
    else:
        print("YES")
        res.sort()
        for i in res:
            print(i, end =" ")