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:
input=__import__('sys').stdin.readline
lis=[0]*32
lis[0]=1
for i in range(1,32):
    lis[i]=2*lis[i-1]
#print(lis)
n,k = map(int,input().split())
ans=[1]*k
if n<k:
    print("NO")
else:
    n-=k
    for i in range(k):
        n+=1
        c=0
        for j in range(31,-1,-1):
            if lis[j]<=n:
                c=lis[j]
                break
#        print(c,n)    
        ans[i]=c
        n-=c
#    print(ans)    
    if n!=0:
        print("NO")
    else:
        print("YES")        
        print(*ans)