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())
if k>n:
    print("NO")
else:
    count=0
    l=bin(n)
    b=l[2:]
    my=[]
    length=len(b)
    for i in range(length):
        num=int(b[i])*(2**(length-1-i))
        if num!=0:
            my.append(num)
            count+=1;
    if k<count:
        print("NO")
    elif k==count:
        print("YES")
        for i in my:
            print(i,end=" ")
    else:
        p=0
        while(1):
            if my[p]!=1:
                my[p]=my[p]//2
                my.append(my[p])
                count+=1
                if count==k:
                    break
            elif my[p]==1:
                p+=1 
            else:
                break
        if count==k:
            print("YES")
            for i in my:
                print(i,end=" ")
        else:
            print("NO")