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Here is a possible C++ implementation for the given problem:

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

long long powerMod(long long base, long long exp, long long mod) {
    long long result = 1;
    while (exp > 0) {
        if (exp % 2 == 1) {
            result = (result * base) % mod;
        }
        base = (base * base) % mod;
        exp /= 2;
    }
    return result;
}

int main() {
    long long x, q, M;
    cin >> x >> q >> M;

    vector<long long> factors(q);
    for (int i = 0; i < q; i++) {
        cin >> factors[i];
    }

    sort(factors.begin(), factors.end());

    long long result = 1;
    for (int i = 0; i < q; i++) {
        result = (result * powerMod(factors[i], x, M)) % M;
        x = factors[i] * x % M;
    }

    cout << result << endl;

    return 0;
}

Explanation:

1. Read the inputs for x, q, and M.
2. Read the q factors and store them in a vector.
3. Sort the factors in increasing order.
4. Iterate over the factors and for each factor, calculate its power modulo M using the powerMod function and multiply it with the current result modulo M.
5. Update the value of x by multiplying it with the current factor modulo M.
6. After the loop, output the final result modulo M