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:
from collections import deque
import sys
input = sys.stdin.readline

n, k = map(int, input().split())
pow2 = [1]
for _ in range(35):
    pow2.append(2 * pow2[-1])
x = []
for i in pow2:
    if i & n:
        x.append(i)
ans = "YES" if len(x) <= k <= n else "NO"
print(ans)
if ans == "YES":
    c = k - len(x)
    q = deque()
    y = []
    while c:
        if not q:
            q.append(x.pop())
        i = q.popleft()
        if i == 1:
            y.append(i)
        else:
            q.append(i // 2)
            q.append(i // 2)
            c -= 1
    for i in y:
        x.append(i)
    for i in q:
        x.append(i)
    print(*x)