题目描述
On an xy plane, in an area satisfying 0 ≤ x ≤ W, 0 ≤ y ≤ H, there is one house at each and every point where both x and y are integers.
There are unpaved roads between every pair of points for which either the x coordinates are equal and the difference between the y coordinates is 1, or the y coordinates are equal and the difference between the x coordinates is 1.
The cost of paving a road between houses on coordinates (i,j) and (i+1,j) is p_i for any value of j, while the cost of paving a road between houses on coordinates (i,j) and (i,j+1) is q_j for any value of i.
Mr. Takahashi wants to pave some of these roads and be able to travel between any two houses on paved roads only. Find the solution with the minimum total cost.
Constraints
- 1 ≦ W,H ≦ 10^5
- 1 ≦ p_i ≦ 10^8(0 ≦ i ≦ W-1)
- 1 ≦ q_j ≦ 10^8(0 ≦ j ≦ H-1)
- p_i (0 ≦ i ≦ W−1) is an integer.
- q_j (0 ≦ j ≦ H−1) is an integer.
Input
Inputs are provided from Standard Input in the following form.
W H
p_0
:
p_{W-1}
q_0
:
q_{H-1}
Output
Output an integer representing the minimum total cost.
Examples
Input
2 2
3
5
2
7
Output
29
Input
4 3
2
4
8
1
2
9
3
Output
60
输入格式
见题面
输出格式
见题面