I want to calculate cos(nx) = p/q Using recursion and memoization so i tried Chebyshev Method for Recursive Method it works for small inputs of n but i want to do it for larger inputs like 10^18 etc. How should i approach it to calculate cos(nx) in p/q Form?

cos(x) = a/b Known

    #include <bits/stdc++.h>      using namespace std;     map<long, long> numerator;     map<long, long> denominator;     #define MODULO 1000000007     long a, b, n;      int main() {         cin >> a >> b;         cin >> n;         numerator[0] = 1;         numerator[1] = a;         denominator[0] = 1;         denominator[1] = b;         for (long i = 2; i <= n; ++i) {             numerator[i] = (long) (2 * a * numerator[i - 1] - b*numerator[i - 2]) % MODULO;             denominator[i] = (denominator[i - 1] * denominator[i - 2]) % MODULO;         }         cout << "numerator of cos(nx) = " << numerator[n] << " denominator = " << denominator[n] << endl;     }