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++14 (GCC 5.4.1) (judge verdict: Accepted)

//let's do it
 #include <iostream>
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
#define inf 1000000000000
#define mod 1000000007
#define pb push_back
#define mp make_pair
#define all(v) v.begin(),v.end()
#define S second
#define F first
#define boost1 ios::sync_with_stdio(false);
#define boost2 cin.tie(0);
#define mem(a,val) memset(a,val,sizeof a)
#define endl "\n"
#define maxn 100001

ll x[maxn],y[maxn];
inline ll add(ll x,ll y)
{
	return (x+y)%mod;
}
inline ll mul(ll x,ll y)
{
	return (x*y)%mod;
}
inline ll sub(ll x,ll y)
{
	return (x-y+mod)%mod;
}
int main()
{
	boost1;boost2;
	ll i,j,n,m,ans=0,sum=0,val=0;
	cin>>n>>m;
	for(i=1;i<=n;i++)
	cin>>x[i];
	for(i=1;i<=m;i++)
	cin>>y[i];
	for(i=1;i<=m;i++)
	{
		val=add(val,mul(y[i],(i-1)));
		val=sub(val,sum);
		sum=add(sum,y[i]);
	}
	sum=0;
	for(i=1;i<=n;i++)
	{
		ans=add(ans,mul(i-1,x[i]));
		ans=sub(ans,sum);
		sum=add(sum,x[i]);
	}
	cout<<mul(ans,val);
	return 0;
}