B - Achieve the Goal

Score : $200$ points

Problem Statement

Takahashi is taking exams on $N$ subjects. The score on each subject will be an integer between $0$ and $K$ (inclusive).

He has already taken exams on $N-1$ subjects and scored $A_i$ points on the $i$-th subject.

His goal is to achieve the average score of $M$ points or above on the $N$ subjects.

Print the minimum number of points Takahashi needs on the final subject to achieve his goal.

If the goal is unachievable, print -1 instead.

Constraints

• $2 \leq N \leq 100$
• $1 \leq K \leq 100$
• $1 \leq M \leq K$
• $0 \leq A_i \leq K$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$ $M$

$A_1$ $A_2$ $...$ $A_{N-1}$

Output

Print the minimum number of points required on the final subject, or -1.

5 10 7
8 10 3 6

8

If he scores $8$ points on the final subject, his average score will be $(8+10+3+6+8)/5 = 7$ points, which meets the goal.

4 100 60
100 100 100

0

Scoring $0$ points on the final subject still meets the goal.

4 100 60
0 0 0

-1

He can no longer meet the goal.