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:
mod = 1000000007
ii = lambda :  int(input())
si = lambda :  input()
dgl = lambda : list(map(int, input()))
f = lambda :   map(int, input().split())
il = lambda :  list(map(int, input().split()))
it = lambda :  tuple(map(int, input().split()))
ls = lambda :  list(input())
n, k = f()
m = n
l = []
x = 1
while x < 10**9:
    l.append(x)
    x=x << 1
res = []
l.reverse()
for i in l:
    while k>0 and (n-i)>=(k-1):
        res.append(i)
        n-=i
        k-=1

if sum(res) != m:
    print('NO')
else:
    print('YES')
    print(*res)