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 
def block(n,k): 
      
    v = [] 
    count=0 
    while ( n> 0): 
        if int(n%2)==1:
            count+=1
        v.append(int(n % 2)) 
        n = int(n / 2) 
    if count==k:
        print("YES")
        for i in range(0, len(v)): 
            if (v[i] == 1): 
                print (2**i, end = " ") 
        exit()
    j=[]
    flag=0
    for i in range(len(v)):
        if v[i]==1:
            j.append(i)
    j.sort(reverse=True)
    d=0
    i=0
    p=len(j)
    while i<k:
        if j[i]==0:
            i+=1
            continue
        j[i]-=1
        j.append(j[i])
        if len(j)==k:
            flag=1
            break
        if j[i]==0:
            i+=1
    if flag==0:
        print("NO")
        exit()
    j.sort()
    print("YES")
    for i in range(len(j)):
        print(2**j[i],end=" ")

def Log2(x): 
    return (math.log10(x) / 
            math.log10(2))
  
def isPowerOfTwo(n): 
    return (math.ceil(Log2(n)) == 
            math.floor(Log2(n))) 

n , k = [int(i) for i in input().split()]
if k==1:
    if(isPowerOfTwo(n)): 
        print("YES")
        print(n)
        exit()
    else:
        print("NO")
        exit()
if n<k:
    print("NO")
    exit()
block(n,k)