CF1316A.Grade Allocation

$n$ students are taking an exam. The highest possible score at this exam is $m$ . Let $a_{i}$ be the score of the $i$ -th student. You have access to the school database which stores the results of all students.

You can change each student's score as long as the following conditions are satisfied:

• All scores are integers
• $0 \leq a_{i} \leq m$
• The average score of the class doesn't change.

You are student $1$ and you would like to maximize your own score.

Find the highest possible score you can assign to yourself such that all conditions are satisfied.

Each test contains multiple test cases.

The first line contains the number of test cases $t$ ( $1 \le t \le 200$ ). The description of the test cases follows.

The first line of each test case contains two integers $n$ and $m$ ( $1 \leq n \leq 10^{3}$ , $1 \leq m \leq 10^{5}$ ) — the number of students and the highest possible score respectively.

The second line of each testcase contains $n$ integers $a_1, a_2, \dots, a_n$ ( $ 0 \leq a_{i} \leq m$ ) — scores of the students.

For each testcase, output one integer — the highest possible score you can assign to yourself such that both conditions are satisfied._

In the first case, $a = [1,2,3,4] $ , with average of $2.5$ . You can change array $a$ to $[10,0,0,0]$ . Average remains $2.5$ , and all conditions are satisfied.

In the second case, $0 \leq a_{i} \leq 5$ . You can change $a$ to $[5,1,1,3]$ . You cannot increase $a_{1}$ further as it will violate condition $0\le a_i\le m$ .