Sequence Sum

AtCoder

IDabc179_e

Time2000ms

Memory256MB

Difficulty—

Let us denote by $f(x, m)$ the remainder of the Euclidean division of $x$ by $m$. Let $A$ be the sequence that is defined by the initial value $A_1=X$ and the recurrence relation $A_{n+1} = f(A_n^2, M)$. Find $\displaystyle{\sum_{i=1}^N A_i}$. ## Constraints * $1 \leq N \leq 10^{10}$ * $0 \leq X < M \leq 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $X$ $M$ [samples]

Samples

Input #1

6 2 1001

Output #1

1369

The sequence $A$ begins $2,4,16,256,471,620,\ldots$ Therefore, the answer is $2+4+16+256+471+620=1369$.

Input #2

1000 2 16

Output #2

6

The sequence $A$ begins $2,4,0,0,\ldots$ Therefore, the answer is $6$.

Input #3

10000000000 10 99959

Output #3

492443256176507

API Response (JSON)

{
  "problem": {
    "name": "Sequence Sum",
    "description": {
      "content": "Let us denote by $f(x, m)$ the remainder of the Euclidean division of $x$ by $m$. Let $A$ be the sequence that is defined by the initial value $A_1=X$ and the recurrence relation $A_{n+1} = f(A_n^2, M",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc179_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let us denote by $f(x, m)$ the remainder of the Euclidean division of $x$ by $m$.\nLet $A$ be the sequence that is defined by the initial value $A_1=X$ and the recurrence relation $A_{n+1} = f(A_n^2, M...",
      "is_translate": false,
      "language": "English"
    }
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}

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