Dorayaki

Interview

Time limit2sMemory limit2048 MB

Summary

Given tastiness values for N fillings and M skins, sum (a+b) times max(a,b) over every filling and skin pair.

Level: Easy2 of 10
Topics: Brute force, Implementation
Solved: No attempts yet

Problem

JOI is making dorayaki.

Each dorayaki is made from exactly one filling and one skin. Every filling and skin has a tastiness value, which is a positive integer. There are N kinds of fillings numbered 1 to N, and the tastiness of filling i is Ai. There are M kinds of skins numbered 1 to M, and the tastiness of skin j is Bj.

JOI tries every combination of filling and skin, making N × M dorayaki. The tastiness of each dorayaki is the sum of its filling and skin tastiness, multiplied by the larger of those two values.

Find the total tastiness of all N × M dorayaki.

Input

The input is given in the following format.

N M
A1 A2 … AN
B1 B2 … BM

Output

Print the total tastiness of all N × M dorayaki.

Print only the answer. Do not print any prompt or other text.

Constraints

1 ≦ N ≦ 100.
1 ≦ M ≦ 100.
1 ≦ Ai ≦ 100 (1 ≦ i ≦ N).
1 ≦ Bj ≦ 100 (1 ≦ j ≦ M).
All input values are integers.

Examples3

Example 1
Input
```
2 2
1 2
2 5
```
Expected output
```
79
```
Example 2
Input
```
1 5
50
9 7 5 4 1
```
Expected output
```
13800
```

Example 3

Input

15 5
5 10 52 31 14 16 19 1 9 20 80 19 11 34 72
20 2 4 9 19

Expected output