Beat the Average CodeChef Solution | CodeChef Problem Solution 2022

Beat the Average CodeChef Solution | CodeChef Problem Solution 2022

There are N$N$ students in a class. Recently, an exam on Advanced Algorithms was conducted with maximum score M$M$ and minimum score 0$0$. The average score of the class was found out to be exactly X$X$.

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Given that a student having score strictly greater than the average receives an A grade, find the maximum number of students that can receive an A grade.

Input Format

• First line will contain T$T$, number of test cases. Then the test cases follow.

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• The only line of each test case consists of three integers N,M,X$N,M,X$ - the number of students, the maximum score and the average score respectively.

Output Format

For each test case, output in a single line, the maximum number of students who can receive A grade.

Constraints

• 1≤T≤1000$1\le T\le 1000$
• 2≤N≤107$2\le N\le {10}^7$
• 1≤X≤M≤100$1\le X\le M\le 100$

Sample Input 1 

4
2 100 50
3 100 50
5 40 40
10 50 49

Sample Output 1 

1
2
0
9

Explanation

Test case 1$1$: There are 2$2$ students in the class. One of the possible values of scores is [99,1]$[99,1]$. Here, the average score is 99+12=1002=50$\frac{99+1}{2}=\frac{100}{2}=50$. Only the first student receives an A grade. It can be shown that the maximum number of students receiving an A grade is not more than 1$1$.

Test case 2$2$: There are 3$3$ students in the class. One of the possible values of the scores is [60,20,70]$[60,20,70]$. Here, the average score is 60+20+703=1503=50$\frac{60+20+70}{3}=\frac{150}{3}=50$. The students receiving an A grade are students 1$1$ and 3$3$. It can be shown that the maximum number of students receiving an A grade is not more than 2$2$.

Test case 3$3$: There are 5$5$ students in the class. The average score and the maximum score is 40$40$. Thus, the scores of all the students is 40$40$. Since the score of all the students is equal to the average, none of them receive an A grade.

Test case 4$4$: It can be shown that the maximum number of students receiving an A grade does not exceed 9$9$.

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