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 = map(int, input().split())
b = []
a = []
for i in range(31):
    a.append(2**i)
for i in range(30,-1,-1):
    q = n-k+1
    counter = 0
    while a[i]<=q:
        n-=a[i]
        k-=1
        counter+=1
        q = n-k+1
        if k==0:
            break
    for j in range(counter):
        b.append(a[i])
    if k==0:
        break
if n==0 and k==0:
    print('YES')
    print(*b)
else:
    print('NO')