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 Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(let* ((n (read))
    (a (make-array n :initial-element 1))
    (ans 0))
    
    (loop for i below n do
        (setf (aref a i) (rem (read) 1000000007))
    )
    (loop for i below (expt 2 n) do
        (let ((flg 0)
            (tmp 1))
            (loop for j below n  do
                (if (= (logand (ash i (- j)) #b1) 1)
                ;;bitが1だった場合の処理
                    (progn
                        (incf flg)
                        (if (<= flg 2)
                            (progn
                                (setq tmp (* tmp (aref a j)))
                                (if (>= tmp 1000000007)
                                    (setq tmp (rem tmp 1000000007))
                                )
                            )
                            (return)
                        )
                    )
                )
            )
            ;;i番目のパターンの処理
            (if (= flg 2)
                (incf ans tmp)
            )
        )
    )
    (format t "~D~%" (rem ans 1000000007))
)