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.

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.

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.

Sample Input 1

5 10 7
8 10 3 6

Sample Output 1

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.

Sample Input 2

4 100 60
100 100 100

Sample Output 2

0

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

Sample Input 3

4 100 60
0 0 0

Sample Output 3

-1

He can no longer meet the goal.

见题面 Input 部分

见题面 Output 部分