Contest Duration: - (local time) (100 minutes) Back to Home
B - Achieve the Goal /

Time Limit: 2 sec / Memory Limit: 1024 MB

制約

• 2 \leq N \leq 100
• 1 \leq K \leq 100
• 1 \leq M \leq K
• 0 \leq A_i \leq K
• 入力中のすべての値は整数である。

入力

N K M
A_1 A_2 ... A_{N-1}


入力例 1

5 10 7
8 10 3 6


出力例 1

8


入力例 2

4 100 60
100 100 100


出力例 2

0


入力例 3

4 100 60
0 0 0


出力例 3

-1


もはや挽回は不可能です。

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.

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.