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:
def binary(n,a):
    if n>1:
        binary(n//2,a)
    a.append(n%2)

n,k=map(int,input().split())
a=[]
binary(n,a)
m1=0
m2=0
a=a[::-1]
ans=[]
m3=0
for i in range(len(a)):
    if a[i]==1:
        m1+=1
        m2+=2**i
        ans.append(2**i)
        m3+=1
if k>=m1 and k<=n:
    print("YES")
    x=k-m3
    i=0
    cnt=0
    while cnt<x:
        if ans[i]!=1:
            ans[i]=ans[i]//2
            ans.append(ans[i])
            cnt+=1
        else:
            i+=1
    print(*ans)
else:
    print("NO")