CF1700A.Optimal Path

You are given a table $a$ of size $n \times m$ . We will consider the table rows numbered from top to bottom from $1$ to $n$ , and the columns numbered from left to right from $1$ to $m$ . We will denote a cell that is in the $i$ -th row and in the $j$ -th column as $(i, j)$ . In the cell $(i, j)$ there is written a number $(i - 1) \cdot m + j$ , that is $a_{ij} = (i - 1) \cdot m + j$ .

A turtle initially stands in the cell $(1, 1)$ and it wants to come to the cell $(n, m)$ . From the cell $(i, j)$ it can in one step go to one of the cells $(i + 1, j)$ or $(i, j + 1)$ , if it exists. A path is a sequence of cells in which for every two adjacent in the sequence cells the following satisfies: the turtle can reach from the first cell to the second cell in one step. A cost of a path is the sum of numbers that are written in the cells of the path.

For example, with $n = 2$ and $m = 3$ the table will look as shown above. The turtle can take the following path: $(1, 1) \rightarrow (1, 2) \rightarrow (1, 3) \rightarrow (2, 3)$ . The cost of such way is equal to $a_{11} + a_{12} + a_{13} + a_{23} = 12$ . On the other hand, the paths $(1, 1) \rightarrow (1, 2) \rightarrow (2, 2) \rightarrow (2, 1)$ and $(1, 1) \rightarrow (1, 3)$ are incorrect, because in the first path the turtle can't make a step $(2, 2) \rightarrow (2, 1)$ , and in the second path it can't make a step $(1, 1) \rightarrow (1, 3)$ .

You are asked to tell the turtle a minimal possible cost of a path from the cell $(1, 1)$ to the cell $(n, m)$ . Please note that the cells $(1, 1)$ and $(n, m)$ are a part of the way.

The first line contains a single integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases. The description of test cases follows.

A single line of each test case contains two integers $n$ and $m$ ( $1 \leq n, m \leq 10^4$ ) — the number of rows and columns of the table $a$ respectively.

For each test case output a single integer — a minimal possible cost of a path from the cell $(1, 1)$ to the cell $(n, m)$ .

In the first test case the only possible path consists of a single cell $(1, 1)$ .

The path with the minimal cost in the second test case is shown in the statement.

In the fourth and the fifth test cases there is only one path from $(1, 1)$ to $(n, m)$ . Both paths visit every cell in the table.