CF1497C2 k-LCM (hard version)

It is the hard version of the problem. The only difference is that in this version $ 3 \le k \le n $ . You are given a positive integer $ n $ . Find $ k $ positive integers $ a_1, a_2, \ldots, a_k $ , such that: - $ a_1 + a_2 + \ldots + a_k = n $ - $ LCM(a_1, a_2, \ldots, a_k) \le \frac{n}{2} $ Here $ LCM $ is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers $ a_1, a_2, \ldots, a_k $ . We can show that for given constraints the answer always exists.

The first line contains a single integer $ t $ $ (1 \le t \le 10^4) $ — the number of test cases. The only line of each test case contains two integers $ n $ , $ k $ ( $ 3 \le n \le 10^9 $ , $ 3 \le k \le n $ ). It is guaranteed that the sum of $ k $ over all test cases does not exceed $ 10^5 $ .

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