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: Wrong Answer)

import qualified Data.Vector.Unboxed as VU
import qualified Data.ByteString.Char8 as B
import Data.Tuple.Extra

main = do
  let readInt = fmap (second B.tail) . B.readInt
  n <- readLn
  xs <- VU.unfoldrN n readInt <$> B.getLine
  print $ solve n xs

solve :: Int -> VU.Vector Int -> Int
solve n xs = VU.foldl (\x y -> (x + y) `mod` (1000000000 + 7)) 0 ys
  where
    ss = VU.scanl (+) 0 xs

    ys = VU.generate n $ \i -> (xs VU.! i) * ((ss VU.! n) - (ss VU.! (i+1)))