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:
import sys

line = sys.stdin.readline().strip().split()
n = int(line[0])
k = int(line[1])
powers = []
p = 0

if n < k:
    print("NO")
else:
    if k > 32:
        powers = [1] * (k-32)
        n = n - k + 32
        k = 32
    while n > 0:
        while n - 1 < 2 ** (k - 1) and n != 0 and k != 0:
            powers.append(2 ** p)
            n = n - 1
            k = k - 1
        if n > 0:
            if n % 2 == 1:
                powers.append(2 ** p)
                n = n - 1
                k = k - 1
            else:
                n = n // 2
                p = p + 1
    if k == 0:
        print("YES")
        print(" ".join(list(map(str, powers))))
    else:
        print("NO")