Background

Translated from ROIR 2021 Day1 T2 Разбиение таблицы。

Problem Description

There is an $n \times m$ number table $a$, where $a_{i,j} = (i - 1) \times m + j$.

Now split this table into two tables $x, y$ so that $\max\{\sum x, \sum y\}$ is minimized.

More concretely, you may choose an $i$, then make one vertical cut between column $i - 1$ and column $i$, or make one horizontal cut between row $i - 1$ and row $i$. The two resulting tables are $x$ and $y$.

Please construct one valid plan.

Input Format

This problem has multiple test cases.

The first line contains an integer $t$.

The next $t$ lines each contain two integers $n, m$, representing the size of the table in this query.

Output Format

For each query, output a character $c$ and an integer $x$.

If you want to cut vertically, let $c$ be V, and let $x$ be your chosen $i$.

If you want to cut horizontally, let $c$ be H, and let $x$ be your chosen $i$.

If there are multiple solutions, output a vertical cut. If there are still multiple solutions, output the one with the smallest $x$.

5
1 3
4 7
1 10
3 3
3 5

V 3
V 5
V 8
H 3
V 4

Hint

Constraints:

For all subtasks, $1 \le t \le 10^5$, $1 \le n, m \le 10^9$, $2 \le n \times m \le 10^9$.

Translated by ChatGPT 5