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())
c=0
s=dict()
ans=[]
r=n
f=0
while(n>0):
    c+=1
    if n%2==1:
        f+=1
        s.update({2**(c-1):1})
    n//=2
#print(s)
n=r
if k>n:
    print("NO")
elif k<f:
    print("NO")
else:
    print("YES")
    r=k-f
    while(r>0):
        for j in s:
            if j!=1:
                if (j//2) not in s:
                    s.update({j//2:2})
                else:
                    s[j//2]+=2
                s[j]-=1
                if s[j]==0:
                    del s[j]
                r-=1
                break 
    #print(s)
    for j in s:
        for k in range(s[j]):
            ans.append(j)
    print(*ans,sep=" ")