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(i) for i in input().split()]
str=bin(n)[2:]
l=[int(i) for i in list(str[::-1])]
p=[]
for i in range(30):
    p.append(2**i)
if str.count("1")>k:
    print("NO")
elif k>n:
    print("NO")
else:
    length=len(l)
    for x in range(k-str.count("1")):
        for i in range(1,length):
            if l[i]:
                l[i]-=1
                l[i-1]+=2
                break
    if sum(l)==k:
        print("YES")
        for i in range(length):
            for x in range(l[i]):
                print(p[i],end=' ')
    else:
        print("NO")