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 Julia (1.4.0) (judge verdict: Accepted)

function main()
    m=10^9+7
    n=myread(Int)
    a=myreads(Int)
    s=zeros(Int,n+1)
    for i=1:n
        s[i+1]=mod(s[i]+a[i],m)
    end
    ans=0
    for i=1:n
        ans=mod(ans+mod(s[end]*a[i],m),m)
        ans=mod(ans-mod(s[i+1]*a[i],m),m)
    end
    println(ans)
end

# ----------input function----------
sread()=chomp(readline())
sreads(sp=" ")=split(readline(),sp)
myread(ty)=parse(ty,sread())
myreads(ty)=parse.(ty,sreads())
main()