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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

import qualified Data.Text.Lazy as T
import qualified Data.Text.Lazy.IO as T
import qualified Data.Text.Lazy.Read as T

main :: IO ()
main = do
  let
    modulus = 1000000007 :: Int
    modAdd :: Int -> Int -> Int
    modAdd x y = (x + y) `mod` modulus
    modMul :: Int -> Int -> Int
    modMul x y = (x * y) `mod` modulus
    go :: Int -> Int -> [Int] -> Int
    go s c (x : xs) = go (s `modAdd` (c `modMul` x)) (c `modAdd` x) xs
    go s c _        = s
  n <- unsafeTextToInt <$> T.getLine :: IO Int
  as <- map unsafeTextToInt . T.words <$> T.getContents :: IO [Int]
  print . go 0 0 $ as

unsafeTextToInt :: T.Text -> Int
unsafeTextToInt s = case T.signed T.decimal s of
  Right (n, _) -> n
{-# INLINE unsafeTextToInt #-}