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:
def minimum_k(x): 
    arr = []
    ans = []

    while x > 0:
        arr.append(x % 2) 
        x //= 2 
  
    for i in range(len(arr)): 
        if arr[i] == 1: 
            ans.append(2**i)
            
    return ans
    
def solve():
    n, k = map(int, input().split())
    
    result = minimum_k(n)
    
    min_len = len(result)
    
    if k < min_len or k > n:
        print ("NO")
        return
    
    i = 0
    
    while min_len < k:
        while result[i] == 1:
            i += 1
            
        x = result[i]//2
        result[i] = x
        result.append(x)
        
        min_len += 1        
    
    print ("YES")
    print (' '.join(str(k) for k in sorted(result)))    

if __name__ == "__main__":
    solve()