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.