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())
if(k>n):print("NO")
else:
    a=bin(n)
    a=a[2:]
    b=[0 for i in range(31)]
    for i in range(len(a)):
        if(a[i]=='1'):b[len(a)-1-i]=1
    if(b.count(1)<=k):
        print("YES")
        for i in range(31):
            if(sum(b)==k):break
            while (b[31-1-i]>0 and sum(b)<k):
                b[31-1-i]-=1
                b[31-i-2]+=2
            i+=1
        c=[]    
        for i in range(31):
            for j in range(b[i]):
                c.append(2**i)
        print(*c)        
    else:
        print("NO")