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=map(int,input().split())
n1=n
mas=[]
while n!=0:
    mas.append(n%2)
    n=n//2
if (sum(mas)>k) or (k>n1):
    print("NO")
else:
    flag=True
    s=sum(mas)
    i=len(mas)-1
    while flag:
        if (s-mas[i])+2*mas[i]<k:
            mas[i-1]+=mas[i]*2
            s+=mas[i]
            mas[i]=0
            i-=1
        else:
            b=k-s
            mas[i]-=b
            mas[i-1]+=2*b
            flag=False
    s=""
    print("YES")
    for i in range(0,i+1):
        for j in range(mas[i]):
            print(2**i,end=" ")