Red and White Ribbon (APCS 2019-02 Advanced)

2.0s 256M

A ribbon has \(n\) cells: red is \(1\) and white is \(0\). Paint \(k\) specified white cells red in order. At each state, consider maximal consecutive red runs. Sum the longest run lengths over the initial state and all states after painting; also sum the shortest lengths. A state with no red cells contributes zero to both.

Input

Read \(n,k\), the \(n\) colors, then \(k\) one-based paint positions. The third line is empty when \(k=0\).

Constraints

\(1\le n\le100000\), \(0\le k\le\min(n,20000)\). Paint positions are distinct initially white cells. Every red run in every state has length at most \(10000\).

Output

Print the longest-length sum, then the shortest-length sum on the next line.

Sample Input 1

5 1
1 0 1 0 1
2

Sample Output 1

4
2

Sample Input 2

9 3
0 1 1 0 0 1 0 1 0
5 1 7

Sample Output 2

11
6

Source

d101 · 2019-02 APCS.

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