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())
s=n-k
c=[]
for i in range(1,35):
    c.append(pow(2,i)-1)
c.reverse()
l=[]
def supress(c,k):
    l=[]
    s=0
    while(k>0):
        if(k>=c[s]):
            k-=c[s]
            l.append(c[s])
        else:
            s+=1
    return l
l=supress(c,s)
if(len(l)>k or s<0):
    print('NO')
else:
    a=[1]*k
    for i in range(len(l)):
        a[i]+=l[i]
    print('YES')
    print(*a)