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 PYTHON):

Solution:
inp = raw_input().split(" ")

sum = int(inp[0])
num = int(inp[1])
ans = []

if sum==num:
   print "YES"
   for i in range(num):
      print 1,
   exit()
if num>sum:
   print "NO"
   exit()
sum = bin(sum)[2:]

for i in range(len(sum)):
   if sum[len(sum)-i-1]=="1":
      ans.append(2**i)
endadd=[]
c=False
while len(ans)<num:
   while len(ans)+len(endadd)<num and len(ans)>0:
      if ans[len(ans)-1]%2==0:
         x = ans[len(ans)-1]/2
         ans.pop()
         endadd += [x,x]
         """if len(ans)>0:
            index = len(ans)-1
            while ans[index]>x:
               endadd.append(ans[index])
               ans.pop()
               index-=1
               if index>len(ans) or index<0:
                  break"""
          
      else:
         endadd.append(ans.pop())   
   ans+=endadd
   endadd = [] 
   #print ans


if len(ans)!=num:
   print "NO"
else:
   print "YES"
   ans.sort()
   print " ".join(map(str,ans))