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
a,b = list(map(int,input().split(' ')))
arr = []
k = 0
while(len(arr)+1<=b):
    arr.append(pow(2,int(math.log2(a))))
    a-=arr[len(arr)-1]
    if(a==0):
        break
tam = len(arr)
if(a==0):
    if(tam==b):
        print("YES")
        print(*arr)
    elif(tam<b):
        while(1):
            e = []
            i = 0
            h = 0
            tam2 = 0
            for i in range(1,tam+1):
                if(arr[i-1]!=1):
                    e.append(int(arr[i-1]/2))
                    e.append(int(arr[i-1]/2))
                    tam2+=2
                else:
                    e.append(arr[i-1])
                    tam2+=1
                if(tam-i+tam2 ==b):
                    arr = e + arr[i:]
                    print("YES")
                    arr.sort()
                    print(*arr)
                    h = 1
                    break
            tam = tam2
            if(h==1):
                break
            arr = e + arr[i:]
            if(list(set(arr))==[1]):
                print("NO")
                break
else:
    print("NO")