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 or k<bin(n)[2:].count("1"):
    print("NO")
else:
    print("YES")
    a=bin(n)[2:][::-1]
    ind=0
    powers=[]
    for char in a:
        if char=="1":
            powers.append(2**ind)
        ind+=1
    ind=0
    tot=len(powers)
    while tot<k:
        if powers[ind]>1:
            powers[ind]//=2
            powers.append(powers[ind])
            tot+=1
        else:
            ind+=1
    out=""
    for guy in powers:
        out+=str(guy)+" "
    print(out)