Chocolate

We are given a bar of chocolate made up of $m \times n$ unit squares, and we want to break it into individual unit squares.

A part of the chocolate can be broken along one of its vertical or horizontal grid lines. A single break splits one part into two smaller parts. The cost of a break depends only on the line it is made along, not on the size of the part being broken. Breaking along vertical line $i$ costs $x_i$ (for $i = 1, 2, \ldots, m-1$), and breaking along horizontal line $j$ costs $y_j$ (for $j = 1, 2, \ldots, n-1$).

For example, for the bar in the picture ($m = 6$, $n = 4$), if we first break along all horizontal lines and then break each resulting strip along the vertical lines, the total cost is $y_1 + y_2 + y_3 + 4 \cdot (x_1 + x_2 + x_3 + x_4 + x_5)$.

The total cost of breaking the whole bar into unit squares is the sum of the costs of all the breaks performed. Write a program that reads the values $x_1, x_2, \ldots, x_{m-1}$ and $y_1, y_2, \ldots, y_{n-1}$ and computes the minimum possible total cost of breaking the whole bar into unit squares.

The first line contains two integers $m$ and $n$ separated by a single space ($2 \le m, n \le 1000$).

Each of the next $m-1$ lines contains one integer $x_i$ ($1 \le x_i \le 1000$), the cost of the $i$-th vertical line.

Each of the following $n-1$ lines contains one integer $y_j$ ($1 \le y_j \le 1000$), the cost of the $j$-th horizontal line.

Print a single integer: the minimum total cost of breaking the whole bar into unit squares.