Who Wins?

Interview

Time limit1sMemory limit1024 MB

Summary

Given two lists of coding skills, count how many cross-team matches HI wins, how many ARC wins, and how many end in a draw.

Level: Easy3 of 10
Topics: Prefix sum, Sorting, Array
Solved: No attempts yet

Problem

HI-ARC is holding a friendly competition at the end of the semester, split into the HI team and the ARC team. The HI team has $N$ members and the ARC team has $M$ members. Every member of one team plays exactly one match against every member of the other team, so the competition consists of $N \times M$ matches. Each participant has a coding skill. In a match, the participant with the higher coding skill wins, and if the two skills are equal, the match is a draw.

Hayak wants to know the results of the competition early. Predict the results for Hayak.

Input

The first line contains the number of HI team members $N$ and the number of ARC team members $M$ , separated by a space. $(1 \leq N, M \leq 100\,000)$

The second line contains a sequence $a$ of length $N$ , the coding skills of the HI team members, separated by spaces. $(1 \leq a_i \leq 100\,000)$

The third line contains a sequence $b$ of length $M$ , the coding skills of the ARC team members, separated by spaces. $(1 \leq b_i \leq 100\,000)$

Output

Print three integers separated by spaces: the number of wins for HI team participants, the number of wins for ARC team participants, and the number of draws.

Examples2

Example 1
Input
```
4 3
1000 90 3 20000
1 3 100000
```
Expected output
```
7 4 1
```
Example 2
Input
```
5 5
1 2 3 4 5
1 2 3 4 5
```
Expected output
```
10 10 5
```