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:
import heapq
n, k = map(int, input().split())
h = [-x for x in range(30) if n & (1 << x)]
h.reverse()
if len(h) > k or n < k:
  print("NO")
  quit()
to_do = k - len(h)
while to_do > 0:
  x = heapq.heappop(h)
  if x == 0:
    print("NO")
    quit()
  for _ in range(2):
    heapq.heappush(h, x + 1)
  to_do -= 1
print("YES")
ans = [1 << -x for x in h]
for x in reversed(ans):
  print(x, end=' ')