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:
t,k=input().split()
t=int(t)
k=int(k)
a=[]
b=[]
l=0
if(k>t):
    print("NO")
else:
    j=0
    while(t>0):
        if(t%2==1):
            a.append(2**j)
            l+=1
        t//=2
        j+=1
    if(k<l):
        print("NO");
    else:
        while(1):
            if(len(a)==k):
                break
            if(a[0]==1):
                a.remove(1)
                b.append(1)
                k-=1
            else:
                x=a[0]//2
                a.remove(a[0])
                a.append(x)
                a.append(x)
        print("YES")
        print(*b,*a)