Takahashi's Basics in Education and Learning

AtCoder

IDabc129_f

Time3000ms

Memory256MB

Difficulty—

There is an arithmetic progression with $L$ terms: $s_0, s_1, s_2, ... , s_{L-1}$. The initial term is $A$, and the common difference is $B$. That is, $s_i = A + B \times i$ holds. Consider the integer obtained by concatenating the terms written in base ten without leading zeros. For example, the sequence $3, 7, 11, 15, 19$ would be concatenated into $37111519$. What is the remainder when that integer is divided by $M$? ## Constraints * All values in input are integers. * $1 \leq L, A, B < 10^{18}$ * $2 \leq M \leq 10^9$ * All terms in the arithmetic progression are less than $10^{18}$. ## Input Input is given from Standard Input in the following format: $L$ $A$ $B$ $M$ [samples]

Samples

Input #1

5 3 4 10007

Output #1

5563

Our arithmetic progression is $3, 7, 11, 15, 19$, so the answer is $37111519$ mod $10007$, that is, $5563$.

Input #2

4 8 1 1000000

Output #2

Input #3

107 10000000000007 1000000000000007 998244353

Output #3

39122908

API Response (JSON)

{
  "problem": {
    "name": "Takahashi's Basics in Education and Learning",
    "description": {
      "content": "There is an arithmetic progression with $L$ terms: $s_0, s_1, s_2, ... , s_{L-1}$. The initial term is $A$, and the common difference is $B$. That is, $s_i = A + B \\times i$ holds. Consider the intege",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc129_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is an arithmetic progression with $L$ terms: $s_0, s_1, s_2, ... , s_{L-1}$.\nThe initial term is $A$, and the common difference is $B$. That is, $s_i = A + B \\times i$ holds.\nConsider the intege...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments