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(n<k):
    print("NO")
else:
    le=len(bin(n))-3
    st=1
    li=[]
    for i in range(le+1):
        if(st&n):
            li.append(st)
        st<<=1
    dif=len(li)-k
    if(dif>0):
        print('NO')
    elif(dif==0):
        print('YES')
        print(*li)
    else:
        dif=abs(dif)
        print('YES')
        stack=[]
        while(dif>0):
            for i in li:
                if(dif==0):
                    print(i,end=' ')
                elif(i==1):
                    print(1,end=' ')
                else:
                    dif-=1
                    stack.append(i//2)
                    stack.append(i//2)
            if(dif==0):
                print(*stack)
            li=stack.copy()
            stack=[]