101794: [AtCoder]ABC179 E - Sequence Sum
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
Score : $500$ points
Problem Statement
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:
$N$ $X$ $M$
Output
Print $\displaystyle{\sum_{i=1}^N A_i}$.
Sample Input 1
6 2 1001
Sample Output 1
1369
The sequence $A$ begins $2,4,16,256,471,620,\ldots$ Therefore, the answer is $2+4+16+256+471+620=1369$.
Sample Input 2
1000 2 16
Sample Output 2
6
The sequence $A$ begins $2,4,0,0,\ldots$ Therefore, the answer is $6$.
Sample Input 3
10000000000 10 99959
Sample Output 3
492443256176507