Not Equal

AtCoder

IDabc209_c

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $C$ of $N$ integers. Find the number of sequences $A$ of $N$ integers satisfying all of the following conditions. * $1 \leq A_i \leq C_i\, (1 \leq i \leq N)$ * $A_i \neq A_j\, (1 \leq i < j \leq N)$ Since the count may be enormous, print it modulo $(10^9+7)$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq C_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $C_1$ $C_2$ $\ldots$ $C_N$ [samples]

Samples

Input #1

2
1 3

Output #1

2

We have two sequences $A$ satisfying all of the conditions: $(1,2)$ and $(1,3)$.  
On the other hand, $A=(1,1)$, for example, does not satisfy the second condition.

Input #2

4
3 3 4 4

Output #2

Input #3

2
1 1

Output #3

0

We have no sequences $A$ satisfying all of the conditions, so we should print $0$.

Input #4

10
999999917 999999914 999999923 999999985 999999907 999999965 999999914 999999908 999999951 999999979

Output #4

405924645

Be sure to print the count modulo $(10^9+7)$.

API Response (JSON)

{
  "problem": {
    "name": "Not Equal",
    "description": {
      "content": "You are given a sequence $C$ of $N$ integers. Find the number of sequences $A$ of $N$ integers satisfying all of the following conditions. *   $1 \\leq A_i \\leq C_i\\, (1 \\leq i \\leq N)$ *   $A_i \\neq ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc209_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $C$ of $N$ integers. Find the number of sequences $A$ of $N$ integers satisfying all of the following conditions.\n\n*   $1 \\leq A_i \\leq C_i\\, (1 \\leq i \\leq N)$\n*   $A_i \\neq ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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