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,k=map(int, input().split(" "))
power1=[int(0)]*k
a1=k-1
ans=0
for i in power1:
        ans+=2**i
def program(power,a):
    global n,ans
    if(a<0): 
        print("NO")
        return (0)
    if(ans==n):
        print("YES")
        for i in power1:
            print(2**i,end=" ")
        return None
    elif(ans<n):
        ans-=2**power[a]
        power[a]+=1
        ans+=2**power[a]
        program(power,a)
    else:
        if(power[a]>0): 
            ans-=2**power[a]
            power[a]-=1
            ans+=2**power[a]
        a-=1
        program(power,a)
program(power1,a1)