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 main():
    arr=input().split()
    total=int(arr[0])
    count=int(arr[1])
    store=[]
    test=1
    while test<=total:
        if test&total:
            store.append(test)
        test*=2
    if len(store)>count:
        print("NO")
    else:
        position=0
        while len(store)!=count:
            if store[position]%2==0:
                store[position]//=2
                store.append(store[position])
            else:
                position+=1
            if position==len(store):
                break
        if len(store)==count:
            print("YES")
            string=""
            for x in store:
                string+=str(x)+" "
            print(string)
        else:
            print("NO")
main()