Single-use Attack CodeChef Solution

Problem

Chef is playing a video game, and is now fighting the final boss.

The boss has $H$ health points. Each attack of Chef reduces the health of the boss by $X$.
Chef also has a special attack that can be used at most once, and will decrease the health of the boss by $Y$.

Chef wins when the health of the boss is $\le 0$.
What is the minimum number of attacks needed by Chef to win?

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• The first and only line of each test case will contain three space-separated integers $H,X,Y$ — the parameters described in the statement.

Output Format

For each test case, output on a new line the minimum number of attacks needed by Chef to win.

Constraints

Sample 1:

4
100 25 40
100 29 45
46 1 2
78 15 78

4
3
45
1

Explanation:

Test case $1$: Chef can attack the boss $4$ times normally. This results in $25+25+25+25=100$ damage, which is enough to defeat the boss.

Test case $2$: Chef can attack the boss $2$ times normally, then use the special attack. This results in $29+29+45=103$ damage, which is enough to defeat the boss.

Test case $3$: Chef can proceed as follows:

• First, use the special attack. This leaves the boss with $46-2=44$ health.
• Then, use $44$ normal attacks to defeat the boss, since each one does $1$ damage.

This takes a total of $44+1=45$ attacks.

Test case $4$: Chef can use the special attack to immediately bring the health of the boss to zero, hence only needing one attack.