Problem:
Score : 500 points

Problem Statement

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 = y_i.
Similarly, among the lines parallel to the y axis, the i-th from the left is represented by x = x_i.

For every rectangle that is formed by these lines, find its area, and print the total area modulo 10^9+7.

That is, for every quadruple (i,j,k,l) satisfying 1\leq i < j\leq n and 1\leq k < l\leq m, find the area of the rectangle formed by the lines x=x_i, x=x_j, y=y_k and y=y_l, and print the sum of these areas modulo 10^9+7.

Constraints

2 \leq n,m \leq 10^5

-10^9 \leq x_1 < ... < x_n \leq 10^9

-10^9 \leq y_1 < ... < y_m \leq 10^9

x_i and y_i are integers.

Input

Input is given from Standard Input in the following format:

n m
x_1 x_2 ... x_n
y_1 y_2 ... y_m

Output

Print the total area of the rectangles, modulo 10^9+7.

Sample Input 1

3 3
1 3 4
1 3 6

Sample Output 1

60

The following figure illustrates this input:

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

Sample Input 2

6 5
-790013317 -192321079 95834122 418379342 586260100 802780784
-253230108 193944314 363756450 712662868 735867677

Sample Output 2

835067060

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdint.h>

#define MOD_VAL ((uint64_t)1000000007)

uint64_t mul_mod(uint64_t a, uint64_t iter, uint64_t mod)
{
    uint64_t tmp = 0;
    for (int i = 0; i < iter; i++) {
        tmp += a;
        tmp %= mod;
    }
    return tmp;
}

uint64_t hoge(uint64_t cnt) {
    uint64_t tmp = 0;
    int32_t pp; /* prev p */
    uint64_t pinc = 0; /* prev inc */
    for (int i = 0; i < cnt; i++) {
        int32_t p;
        uint64_t w;
        uint64_t inc;
        scanf("%d", &p);
        if (i == 0) {
            pp = p;
            continue;
        }
        w = (uint64_t)(p - pp);
#if 0
        if (w >= MOD_VAL / i) { /* assert */
            printf("assertion failed\n");
            printf("w = %u\n", w);
            printf("i = %u\n", i);
            while(1);
        }
        inc = pinc + (uint64_t)i * w;
#endif
        // printf("w * i = %lu\n", w * i);
        // printf("mul_mod(w, i, MOD_VAL) = %lu\n", mul_mod(w, i, MOD_VAL));

        // inc = pinc + mul_mod(w, i, MOD_VAL);
        inc = pinc + (uint64_t)i * w;
        inc %= MOD_VAL;
        tmp += inc;
        tmp %= MOD_VAL;
        /* save as previous value */
        pp = p;
        pinc = inc;
    }
    return (uint64_t)tmp;
}

int main(void)
{
    uint64_t n, m;
    scanf("%lu %lu", &n, &m);
    printf("%lu\n", (hoge(n) * hoge(m)) % MOD_VAL);
    return 0;
}