Locker Allocation (APCS 2018-10 Expert)

2.0s 256M

There are \(M\) lockers, and \(N\) existing customers rent \(x_i\) lockers each. A new customer needs \(S\) free lockers. You may cancel existing rentals, but each customer must be canceled entirely or retained entirely. Find the minimum total number of rented lockers to cancel so that at least \(S\) lockers become free. The answer is \(0\) if enough lockers are already free.

Input Format

The first line contains \(M,S,N\), in that order. The second contains the \(N\) rental sizes \(x_i\).

Output Format

Print the minimum number of rented lockers that must be canceled.

Constraints

\(1\le M\le100000\), \(1\le S\le M\), \(1\le N\le100\), \(x_i\ge0\), \(\sum x_i\le M\).

Sample Input

20 14 5
1 7 2 8 2

Sample Output

15

Source

APCS 2018-10 public archive version: e465。

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