Problem:
Score : 300 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

Find the sum of A_i \times A_j over all pairs (i,j) such that 1\leq i < j \leq N, modulo (10^9+7).

Constraints

2 \leq N \leq 2\times 10^5

0 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

Print \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} A_i A_j, modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

11

We have 1 \times 2 + 1 \times 3 + 2 \times 3 = 11.

Sample Input 2

4
141421356 17320508 22360679 244949

Sample Output 2

437235829

Solution in Lua (Lua 5.3.5) (judge verdict: Accepted)

local read = io.read

local n = read("n")
local a = {}
for i = 1, n do
	a[i] = read("n")
end

local mod_num = 1000000007

local back_sum_t = {}
back_sum_t[n + 1] = 0
for i = n, 2, -1 do
	back_sum_t[i] = (a[i] + back_sum_t[i + 1]) % mod_num
end
local out = 0
for i = 1, n - 1 do
	out = (out + ((a[i] * back_sum_t[i + 1]) % mod_num)) % mod_num
end

print(out)