Sum of Large Numbers

AtCoder

IDabc163_d

Time2000ms

Memory256MB

Difficulty—

We have $N+1$ integers: $10^{100}$, $10^{100}+1$, ..., $10^{100}+N$. We will choose $K$ or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo $(10^9+7)$. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $1 \leq K \leq N+1$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

3 2

Output #1

10

The sum can take $10$ values, as follows:

*   $(10^{100})+(10^{100}+1)=2\times 10^{100}+1$
*   $(10^{100})+(10^{100}+2)=2\times 10^{100}+2$
*   $(10^{100})+(10^{100}+3)=(10^{100}+1)+(10^{100}+2)=2\times 10^{100}+3$
*   $(10^{100}+1)+(10^{100}+3)=2\times 10^{100}+4$
*   $(10^{100}+2)+(10^{100}+3)=2\times 10^{100}+5$
*   $(10^{100})+(10^{100}+1)+(10^{100}+2)=3\times 10^{100}+3$
*   $(10^{100})+(10^{100}+1)+(10^{100}+3)=3\times 10^{100}+4$
*   $(10^{100})+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+5$
*   $(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+6$
*   $(10^{100})+(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=4\times 10^{100}+6$

Input #2

200000 200001

Output #2

1

We must choose all of the integers, so the sum can take just $1$ value.

Input #3

141421 35623

Output #3

220280457

API Response (JSON)

{
  "problem": {
    "name": "Sum of Large Numbers",
    "description": {
      "content": "We have $N+1$ integers: $10^{100}$, $10^{100}+1$, ..., $10^{100}+N$. We will choose $K$ or more of these integers. Find the number of possible values of the sum of the chosen numbers, 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": "abc163_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N+1$ integers: $10^{100}$, $10^{100}+1$, ..., $10^{100}+N$.\nWe will choose $K$ or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo $(10^9+7)...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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