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())

bin_exp = [int(x) for x in list(bin(n)[2:])]
if k > n or k < bin_exp.count(1):
    print('NO')
else:
    print('YES')
    while sum(bin_exp) < k:
        bin_exp[0] = bin_exp[0] - 1
        bin_exp[1] = bin_exp[1] + 2
        if bin_exp[0] == 0:
            del bin_exp[0]
    ans = ''
    for x in range(len(bin_exp)):
        ans += (str(2 ** (len(bin_exp)-1 - x)) + ' ') * bin_exp[x]
    print(ans[:-1])