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}.

Examples

Input

6 2 1001


Output

1369


Input

1000 2 16


Output

6


Input

10000000000 10 99959


Output

492443256176507
#include <bits/stdc++.h>

int main(){
    using namespace std;
    unsigned long N, X, M, S{0};
    cin >> N >> X >> M;
    vector<pair<unsigned long, unsigned long>> memo(M);
    for(unsigned long i{0}; i < N; ++i){
        if(memo[X].first){
            const auto t{i - memo[X].first}, c{(N - i - 1) / t};
            i += t * c;
            S += (S - memo[X].second) * c;
        }else memo[X] = {i, S};
        S += X;
        (X *= X) %= M;
    }
    cout << S << endl;
}
