A15770. Long Legs

A robot is placed in a cell $(0, 0)$ of an infinite grid. This robot has adjustable length legs. Initially, its legs have length $1$ .

Let the robot currently be in the cell $(x, y)$ and have legs of length $m$ . In one move, it can perform one of the following three actions:

- jump into the cell $(x + m, y)$ ;
- jump into the cell $(x, y + m)$ ;
- increase the length of the legs by $1$ , i. e. set it to $m + 1$ .

What's the smallest number of moves robot has to make to reach a cell $(a, b)$ ?

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

The only line of each test case contains two integers $a$ and $b$ ( $1 \le a, b \le 10^9$ ) — the ending cell.

For each test case, print a single integer — the smallest number of moves the robot is required to make to reach a cell $(a, b)$ from a cell $(0, 0)$ .

In the first testcase, the robot can first jump to $(0, 1)$ , then to $(1, 1)$ . If it ever increases the length of its legs, it will only be able to jump past $(1, 1)$ .

In the second testcase, the robot can jump to $(1, 0)$ , then increase the length of its length to $2$ and jump three times to reach $(1, 6)$ .

In the third testcase, the robot can increase the length of its legs three times to make it $4$ . Then jump to $(0, 4)$ . Then jump twice to reach $(8, 4)$ .