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:
    a=[]
    f = n
    summ=0
    i=0
    while n!=0:
        if n%2!=0:
            a.append(i)
        n//=2
        i+=1
    if len(a)>k:
        print('NO')
    else:
        a.sort()
        c=dict()
        for i in a:
            if i in c:
                c[i]+=1
            else:
                c[i]=1
        summ=len(a)
        while summ!=k:
            if c[max(c.keys())]==0:
                c.pop(max(c.keys()))
            else:
                summ+=1
                x = max(c.keys())
                c[max(c.keys())]-=1
                if x-1 in c:
                    c[x-1]+=2
                else:
                    c[x-1]=2
        a=[]
        for i in c.keys():
            for j in range(c[i]):
                a.append(i)
        a.sort()
        print('YES')
        x=2**a[0]
        print(x, end=' ')
        for i in range(1, len(a)):
            for i in range(a[i]-a[i-1]):
                x*=2
            print(x, end=' ')