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 = int(input())
from collections import deque
def decompose(num):
   bs = '{:b}'.format(num)
   p = len(bs)-1
   ans = []
   for el in bs:
      if el == '1':
         ans.append(2**p)
      p-=1
   return ans

def calc(num):
   return '{:b}'.format(num).count('1')

def minp2(num):
   bs = '{:b}'.format(num)
   l = len(bs)
   bs = bs[::-1]
   for i in range(0,l-1):
      if bs[i] =='1':
         return 2**i
   return num//2

n,k = [int(x) for x in input().split()]

if n<k or calc(n)>k:
   print('NO')
else:
   print('YES')
   terms = deque(decompose(n))
   #print(terms)
   while k>len(terms):
      new = terms.popleft()
      if new==1:
         k-=1
         print(1,end=' ')
      elif new==2:
         print(1,1,end=' ')
         k-=2
      else:
         terms.append(new//2)
         terms.append(new//2)
         #print(terms)
   print(*terms)