Sum of product of pairs

AtCoder

IDabc177_c

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3
1 2 3

Output #1

11

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

Input #2

4
141421356 17320508 22360679 244949

Output #2

437235829

API Response (JSON)

{
  "problem": {
    "name": "Sum of product of pairs",
    "description": {
      "content": "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 $(10^9+7)$.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc177_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are $N$ integers $A_1,\\ldots,A_N$.\nFind the sum of $A_i \\times A_j$ over all pairs $(i,j)$ such that $1\\leq i < j \\leq N$, modulo $(10^9+7)$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 2\\times 10^5$\n* ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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