10706: ABC129 —— F - Takahashi's Basics in Education and Learning
[Creator : ]
Description
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 $M$?
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 $M$?
Input
Input is given from Standard Input in the following format:
```
$L$ $A$ $B$ $M$
```
```
$L$ $A$ $B$ $M$
```
Output
Print the remainder when the integer obtained by concatenating the terms 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 $10^{18}$.
- $1 \leq L, A, B < 10^{18}$
- $2 \leq M \leq 10^9$
- All terms in the arithmetic progression are less than $10^{18}$.
Sample 1 Input
5 3 4 10007
Sample 1 Output
5563
Our arithmetic progression is $3, 7, 11, 15, 19$, so the answer is $37111519$ mod $10007$, that is, $5563$.
Sample 2 Input
4 8 1 1000000
Sample 2 Output
891011
Sample 3 Input
107 10000000000007 1000000000000007 998244353
Sample 3 Output
39122908