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,c=map(int,input().split())
if bin(n).count('1')>c or n<c:
    print('NO')
else:
    a=[]
    s=bin(n)[2:]
    s=s[::-1]
    for i in range(len(s)):
        if s[i]=='1':
            a.append(2**i)
    a.sort()
    while len(a)<c and a[-1]!=1:
        x=a.pop()
        b=[x//2,x//2]
        while len(a)>0 and a[-1]==x and len(a)+len(b)<c and a[-1]!=1:
            a.pop()
            b+=[x//2,x//2]
        a+=b
    if len(a)==c:
        print('YES')
        print(*a)
    else:
        print('NO')