A computer system maintains an LRU (Least Recently Used) cache capable of storing at most K pages.

You are given a sequence of page requests. Initially, the cache is empty.

For every requested page:

• If the page is already present in the cache, it is a cache hit.

  • Mark it as the most recently used page.

• Otherwise, it is a cache miss.

  • If the cache is not full, insert the page.
  • Otherwise, remove the least recently used page and insert the requested page.

After processing all requests, determine the total number of cache hits and cache misses.

Input Format

• The first line contains two integers K and N — the cache capacity and the number of page requests.
• The second line contains N integers representing the page requests.

Output Format

Print two integers:

hits misses

Constraints

• 1 ≤ K ≤ 10^5
• 1 ≤ N ≤ 2 × 10^5
• 1 ≤ pages[i] ≤ 10^9

Sample Input 1

3 8
1 2 3 1 4 5 1 2

Sample Output 1

2 6

Explanation

Request	Cache	Result
1	1	Miss
2	1 2	Miss
3	1 2 3	Miss
1	2 3 1	Hit
4	3 1 4	Miss
5	1 4 5	Miss
1	4 5 1	Hit
2	5 1 2	Miss

Hence, there are 2 hits and 6 misses.

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Sample Input 2

2 6
1 2 3 4 5 6

Sample Output 2

0 6

Explanation

Every request is for a new page, so every access results in a cache miss.