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 = list(map(int,input().strip().split()))
s="{0:b}".format(n)
#print(s)
A=[]
if(k>n):
    print("NO")
else:
    for i,bit in enumerate(reversed(s)):
        if(bit=='1'):
            A.append(-i)
    import heapq 
    heapq.heapify(A)
    #print(A)
    if(len(A)<=k):
        print("YES")
        diff=k-len(A)
        while(diff>0):
            m=heapq.heappop(A)
            heapq.heappush(A,m+1)
            heapq.heappush(A,m+1)
            diff-=1
        print(" ".join(map(lambda x:str(2**-x),reversed(sorted(A)))))
    else:
        print("NO")