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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

// Sum of product of pairs

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func calcProduct(a []int64) int64 {
	const M = 1000000007
	var s int64
	s = 0
	for i := 0; i < len(a)-1; i++ {
		var ps int64
		ps = 0
		for j := i + 1; j < len(a); j++ {
			ps += a[j]
			if M < ps {
				ps -= M
			}
		}
		s += a[i] * ps
		s %= M
	}
	return s
}

func nextInt(sc *bufio.Scanner) (int, error) {
	sc.Scan()
	t := sc.Text()
	return strconv.Atoi(t)
}

func nextInt64(sc *bufio.Scanner) (int64, error) {
	sc.Scan()
	t := sc.Text()
	return strconv.ParseInt(t, 10, 64)
}

func nextString(sc *bufio.Scanner) string {
	sc.Scan()
	return sc.Text()
}

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	n, _ := nextInt(sc)

	a := make([]int64, n)
	for i := 0; i < n; i++ {
		aa, _ := nextInt64(sc)
		a[i] = aa
	}

	r := calcProduct(a)
	fmt.Println(r)
}