A16335 | Treasure Chest

Monocarp has found a treasure map. The map represents the treasure location as an OX axis. Monocarp is at $0$ , the treasure chest is at $x$ , the key to the chest is at $y$ .

Obviously, Monocarp wants to open the chest. He can perform the following actions:

- go $1$ to the left or $1$ to the right (spending $1$ second);
- pick the key or the chest up if he is in the same point as that object (spending $0$ seconds);
- put the chest down in his current point (spending $0$ seconds);
- open the chest if he's in the same point as the chest and has picked the key up (spending $0$ seconds).

Monocarp can carry the chest, but the chest is pretty heavy. He knows that he can carry it for at most $k$ seconds in total (putting it down and picking it back up doesn't reset his stamina).

What's the smallest time required for Monocarp to open the chest?

The first line contains a single integer $t$ ( $1 \le t \le 100$ ) — the number of testcases.

The only line of each testcase contains three integers $x, y$ and $k$ ( $1 \le x, y \le 100$ ; $x \neq y$ ; $0 \le k \le 100$ ) — the initial point of the chest, the point where the key is located, and the maximum time Monocarp can carry the chest for.

For each testcase, print a single integer — the smallest time required for Monocarp to open the chest.