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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.NoSuchElementException;

public class Main {
	static FastScanner sc = new FastScanner();
	static PrintStream out = System.out;

	public static void main(String args[]) {
		int W = ni();
		int H = ni();
		int p[] = na(W);
		int q[] = na(H);

		System.out.println(f(0, 0, W, H, p, q));
	}

	private static long f(int x0, int y0, int x1, int y1, int p[], int q[]) {
		if (x0 == x1) {
			long ret = 0;
			for (int y=y0;y<y1;y++) {
				ret += q[y];
			}
			return ret;
		} else if (y0 == y1) {
			long ret = 0;
			for (int x=x0;x<x1;x++) {
				ret += p[x];
			}
			return ret;
		}

		int maxX = 0;
		int maxY = 0;
		int maxXidx = 0;
		int maxYidx = 0;
		for (int x=x0;x<x1;x++) {
			if (maxX < p[x]) {
				maxX = p[x];
				maxXidx = x;
			}
		}
		for (int y=y0;y<y1;y++) {
			if (maxY < q[y]) {
				maxY = q[y];
				maxYidx = y;
			}
		}

		if (maxX > maxY) {
			long ret = f(x0, y0, maxXidx, y1, p, q) + f(maxXidx+1, y0, x1, y1, p, q) + maxX;
			/*
			System.out.printf("f(%d,%d,%d,%d) = %2d (f(%d,%d,%d,%d) + f(%d,%d,%d,%d), %d)\n", x0, y0, x1, y1, ret,
					x0, y0, maxXidx, y1,
					maxXidx+1, y0, x1, y1,
					maxX);
					*/
			return ret;
		} else {
			long ret = f(x0, y0, x1, maxYidx, p, q) + f(x0, maxYidx+1, x1, y1, p, q) + maxY;
			/*
			System.out.printf("f(%d,%d,%d,%d) = %2d (f(%d,%d,%d,%d) + f(%d,%d,%d,%d): %d)\n", x0, y0, x1, y1, ret,
					x0, y0, x1, maxYidx,
					x0, maxYidx+1, x1, y1,
					maxY);
					*/
			return ret;
		}
	}

	private static String next() {
		return sc.next();
	}

	private static int ni() {
		return sc.nextInt();
	}

	private static long nl() {
		return sc.nextLong();
	}

	private static int[] na(int n) {
		int[] a = new int[n];
		for(int i = 0;i < n;i++) a[i] = ni();
		return a;
	}

	private static long[] nal(int n) {
		long[] a = new long[n];
		for(int i = 0;i < n;i++) a[i] = ni();
		return a;
	}

    private static double nd() {
        return Double.parseDouble( next() );
    }
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
    public boolean hasNext() { skipUnprintable(); return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public int nextInt() {
        if (!hasNext()) throw new NoSuchElementException();
        int n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
}