Machine Rental (APCS 2023-01 Expert)

2.0s 256M

You have \(k\) identical machines and \(n\) rental requests. Request \(i\) occupies one machine throughout the closed interval \([L_i,R_i]\). A machine can serve at most one request at any time. Select and assign requests to maximize the number accepted.

Input Format

The first line contains \(n,k\). The second line contains the \(n\) starting times \(L_i\), and the third line contains the corresponding ending times \(R_i\).

Output Format

Print the maximum number of accepted requests.

Constraints

\(1\le n\le100000\), \(1\le k\le100\), \(0\le L_i\le R_i\le10^8\). After a rental ends at time \(R\), the next rental on that machine must start strictly after \(R\).

Scoring

  • 20 points: \(n\le100\), \(k=1\).
  • 20 points: \(k=1\).
  • 60 points: No additional restrictions.

Each scored test is worth 5 points.

Sample Input 1

5 1
0 2 1 3 4
2 3 5 4 6

Sample Output 1

2

Sample Input 2

8 2
3 1 4 3 7 2 2 5
5 3 7 4 8 7 4 6

Sample Output 2

5

Sample Input 3

2 1
1 2
2 3

Sample Output 3

1

Source

APCS 2023-01 public archive version: j608。

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