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:
def ii():
    return int(input())
def mi():
    return map(int, input().split())
def li():
    return list(mi())

n, k = mi()
if k < bin(n).count('1') or k > n:
    print('NO')
else:
    ans = []
    cur = bin(n).count('1')
    for i in range(30):
        if n >> i & 1:
            st = [1 << i]
            while cur < k and st:
                r = st.pop()
                if r == 1:
                    ans.append(r)
                    continue
                st.append(r >> 1)
                st.append(r >> 1)
                cur += 1
            ans.extend(st)
    print('YES')
    print(*ans)