Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

2 2
3
5
2
7

Sample Output 1

29

It is enough to pave the following eight roads.

Road connecting houses at (0,0) and (0,1)

Road connecting houses at (0,1) and (1,1)

Road connecting houses at (0,2) and (1,2)

Road connecting houses at (1,0) and (1,1)

Road connecting houses at (1,0) and (2,0)

Road connecting houses at (1,1) and (1,2)

Road connecting houses at (1,2) and (2,2)

Road connecting houses at (2,0) and (2,1)

Sample Input 2

4 3
2
4
8
1
2
9
3

Sample Output 2

60

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import defaultdict
from heapq import *
from array import *

def read():
    return int(input())

def reads(sep=None):
    return list(map(int, input().split(sep)))

def mst_prim(adj, n):
    pred = defaultdict(lambda: -1)
    key = defaultdict(lambda: float('inf'))
    key[0] = 0
    pq = [(key[v], v) for v in range(n)]
    heapify(pq)
    in_pq = array('B', (True for _ in range(n)))
    while pq:
        _,u = heappop(pq)
        in_pq[u] = False
        for v, v_cost in adj[u]:
            if in_pq[v]:
                weight = v_cost
                if weight < key[v]:
                    pred[v] = u
                    key[v] = weight
                    heappush(pq, (weight, v))
                    in_pq[v] = True
    return (pred, key)

def main():
    w, h = reads()
    p = [read() for _ in range(w)]
    q = [read() for _ in range(h)]

    adj = defaultdict(set)
    for x in range(w+1):
        for y in range(h+1):
            if x < w:
                adj[x+y*(w+1)].add((x+1+y*(w+1), p[x]))
                adj[x+1+y*(w+1)].add((x+y*(w+1), p[x]))
            if y < h:
                adj[x+y*(w+1)].add((x+(y+1)*(w+1), q[y]))
                adj[x+(y+1)*(w+1)].add((x+y*(w+1), q[y]))
    print(sum(mst_prim(adj, (w+1)*(h+1))[1].values()))

main()