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, m = map(int, input().split())
if n < m:
    print("NO")
    exit()
mas = [int(2 ** i) for i in range(31)]
i = 30
while n < mas[i]:
    i -= 1
ans = []
while n != 0:
    if n - mas[i] >= 0:
        n -= mas[i]
        ans.append(mas[i])
    else:
        i -= 1
ans.sort()
if len(ans) > m:
    print("NO")
    exit()
else:
    i = 0
    while len(ans) != m:       
        if ans[i] != 1:
            ans[i] //= 2
            ans.append(ans[i])
        else:
            i += 1
print("YES")
print(*ans)