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 math
n,k = map(int,input().split())
bi = bin(n)[2:]
l = len(bi)-1
po = []
for i in range(len(bi)):
    if bi[i] == "1":
        po.append(pow(2,l-i))
#print(po)
if(k < len(po) or k>n):
    print("NO")
else:
    ans = []
    j = 0
    while(j<len(po)):
        i = po[j]
        le = k - (len(po)-j-1)
        #print(i,k)
        if(i<=le):
            s = "1 "*i
            ans.append(s)
            le-=i
            k-=i
        elif(le != 0):
            #print(i,le)
            if(i % le == 0):
                dig = str(i//le)
                ans.append(((dig)+" ")*le)
                le = 0
            else:
                base = (pow(2,math.floor(math.log(le,2))))
                lt = (le - int(base))*2
                gt = le - lt
               # print(base,lt,gt)
                dig = str(i//base)
                less = str(int(dig)//2)
                
                
                ans.append((dig+" ")*gt)
                ans.append((less+" ")*lt)
                le = 0
       
                
                
                
              
        if(le == 0): break
        j+=1
    #print(j)
    for i in range(j+1,len(po)):
        ans.append(str(po[i])+" ")
        #continue
        
                
                
       
    print("YES")       
    print("".join(ans))