Problem: It is the hard version of the problem. The only difference is that in this version 3 ≤ k ≤ n.

You are given a positive integer n. Find k positive integers a_1, a_2, …, a_k, such that:

  * a_1 + a_2 + … + a_k = n 
  * LCM(a_1, a_2, …, a_k) ≤ n/2 



Here LCM is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers a_1, a_2, …, a_k.

We can show that for given constraints the answer always exists.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The only line of each test case contains two integers n, k (3 ≤ n ≤ 10^9, 3 ≤ k ≤ n).

It is guaranteed that the sum of k over all test cases does not exceed 10^5.

Output

For each test case print k positive integers a_1, a_2, …, a_k, for which all conditions are satisfied.

Example

Input


2
6 4
9 5


Output


1 2 2 1 
1 3 3 1 1 

Solution (in PYTHON3):

Solution:
t = int(input())


def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)


def sea(n):
    #1 2 3 4
    #1 2 1 [2]  1 2 1 [4] 1 2 1 [6]
    a = [0, 1, 2, 1]
    i = n // 2 if n % 4 == 0 else a[n % 4]
    a = (n - i) // 2
    return [i, a, a]
    # for i in range(1, n // 2 + 1):
    #     if (n - i) % 2 != 0:
    #         continue
    #     a = (n - i) // 2
    #     # print(a, a, i)
    #     if a * i // gcd(a, i) <= n // 2:
    #         return [i, a, a]


def get(n, k):
    res = [1] * k
    tmp = sea(n - k + 3)
    for i in range(3):
        res[i] = tmp[i]
    return res


for _ in range(t):
    n, k = list(map(int, input().split(' ')))
    res = get(n, k)
    print(' '.join(map(str, res)))

# 8 8 4

# 20 3

# 26