Grasshopper on a Line
Description
You are given two integers $x$ and $k$. Grasshopper starts in a point $0$ on an OX axis. In one move, it can jump some integer distance, that is not divisible by $k$, to the left or to the right.
What's the smallest number of moves it takes the grasshopper to reach point $x$? What are these moves? If there are multiple answers, print any of them.
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.
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.
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.
3
10 2
10 3
3 4
2
7 3
1
10
1
3