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C - Sum of product of pairs

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 $(10^9+7)$.

3
1 2 3

11

We have $1 \times 2 + 1 \times 3 + 2 \times 3 = 11$.

4
141421356 17320508 22360679 244949

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