[Solution] Building Race CodeChef Solution

Problem

Two friends Chef and Chefina are currently on floors $A$ and $B$ respectively. They hear an announcement that prizes are being distributed on the ground floor and so decide to reach the ground floor as soon as possible.

Chef can climb down $X$ floors per minute while Chefina can climb down $Y$ floors per minute. Determine who will reach the ground floor first. In case both reach the ground floor together, print Both.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• The first line of each test case contains four space-separated integers $A$, $B$, $X$, and $Y$ — the current floor of Chef, the current floor of Chefina, speed of Chef and speed of Chefina in floors per minute respectively.

Output Format

For each test case, output on a new line:

• Chef if Chef reaches the ground floor first.
• Chefina if she reaches the ground floor first.
• Both if both reach the ground floor at the same time.

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You may print each character of the string in uppercase or lowercase. For example, the strings CHEF, chef, Chef, and chEF are all considered the same.

Explanation:

Test case $1$: Chef is on the second floor and has a speed of $2$ floors per minute. Thus, Chef takes $1$ minute to reach the ground floor. Chefina is on the second floor and and has a speed of $2$ floors per minute. Thus, Chefina takes $1$ minute to reach the ground floor. Both Chef and Chefina reach the ground floor at the same time.

Test case $2$: Chef is on the fourth floor and has a speed of $1$ floor per minute. Thus, Chef takes $4$ minute to reach the ground floor. Chefina is on the second floor and and has a speed of $5$ floors per minute. Thus, Chefina takes $0.4$ minutes to reach the ground floor. Chefina reaches the ground floor first.

Test case $3$: Chef is on the third floor and has a speed of $4$ floors per minute. Thus, Chef takes $0.75$ minutes to reach the ground floor. Chefina is on the second floor and and has a speed of $1$ floor per minute. Thus, Chefina takes $2$ minutes to reach the ground floor. Chef reaches the ground floor first.

Test case $4$: Chef is on the third floor and has a speed of $2$ floors per minute. Thus, Chef takes $1.5$ minutes to reach the ground floor. Chefina is on the second floor and and has a speed of $1$ floor per minute. Thus, Chefina takes $2$ minutes to reach the ground floor. Chef reaches the ground floor first.