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Problem Statement

There are $N$ people, and the current hair length of the $i$-th person $(1 \le i \le N)$ is $L_i$.

Each person's hair grows by $1$ per day.

Print the number of days after which the number of people whose hair length is at least $T$ becomes $P$ or more for the first time.

If there are already $P$ or more people whose hair length is at least $T$ now, print $0$.

Constraints

• $1 \le N \le 100$
• $1 \le L_i \le 100$
• $1 \le T \le 100$
• $1 \le P \le N$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N T P
L1 L2 L3 ... LN

Output

Print the number of days after which the number of people whose hair length is at least $T$ becomes $P$ or more for the first time. If this condition is already satisfied now, print $0$.

Sample

5 10 3
3 11 1 6 2

7

There are five people, and their current hair lengths are $3,11,1,6,2$, so there is one person whose hair length is at least $10$.

After seven days, the hair lengths of the people will be $10,18,8,13,9$, respectively, and there will be three people whose hair length is at least $10$.

After six days, there are only two people whose hair length is at least $10$, not satisfying the condition, so print $7$.

2 5 2
10 10

0

Since there are already two people whose hair length is at least $5$ now, satisfying the condition, so print $0$.

3 10 1
1 2 3

7