Grasshopper on a Line

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of testcases.

The only line of each testcase contains two integers $$$x$$$ and $$$k$$$ ($$$1 \le x \le 100$$$; $$$2 \le k \le 100$$$) — the endpoint and the constraint on the jumps, respectively.

Output:

For each testcase, in the first line, print a single integer $$$n$$$ — the smallest number of moves it takes the grasshopper to reach point $$$x$$$.

In the second line, print $$$n$$$ integers, each of them not divisible by $$$k$$$. A positive integer would mean jumping to the right, a negative integer would mean jumping to the left. The endpoint after the jumps should be exactly $$$x$$$.

Each jump distance should be from $$$-10^9$$$ to $$$10^9$$$. In can be shown that, for any solution with the smallest number of jumps, there exists a solution with the same number of jumps such that each jump is from $$$-10^9$$$ to $$$10^9$$$.

It can be shown that the answer always exists under the given constraints. If there are multiple answers, print any of them.

Sample Input:

3
10 2
10 3
3 4

Sample Output:

2
7 3
1
10
1
3