On a two-dimensional plane, there are m lines drawn parallel to the x axis, and n lines drawn parallel to the y axis. Among the lines parallel to the x axis, the i-th from the bottom is represented by y = yi. Similarly, among the lines parallel to the y axis, the i-th from the left is represented by x = xi.

For every rectangle that is formed by these lines, find its area, and print the total area modulo 109 + 7.

That is, for every quadruple (i, j, k, l) satisfying 1 ≤ i< j ≤ n and 1 ≤ k < l ≤ m, find the area of the rectangle formed by the lines x = xi, x = xj, y = yk and y = yl, and print the sum of these areas modulo 109 + 7.

Input

The first line contains two integers n and m (2 ≤ n, m ≤ 105).

The second line contains n integers -109 ≤ x1 < x2 < ... < xn ≤ 109.

The third line contains m integers -109 ≤ y1, y2, ..., ym ≤ 109.

Output

Print the total area of the rectangles, modulo 109 + 7.

Example

The following figure illustrates this input:

The total area of the nine rectangles A, B, ..., I shown in the following figure, is 60.