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=[int(j) for j in input().split()]
x=bin(n)[2:]
q=x.count("1")
res=[]
if k<q or k>n:
    print("NO")
else:
    print("YES")
    x=[int(j) for j in x]
    r=0
    c=k-q
    while c>0:
        while x[r]==0:
            r+=1
        x[r]-=1
        x[r+1]+=2
        c-=1
    x=x[::-1]
    res=""
    for i in range(len(x)):
        for j in range(x[i]):
            res+=str(2**i)+" "
    print(res[:-1])