#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
int main() {
    LL base = 34;   // 数字n
    int digits = 2; // 后2位
    LL mod = 100;
    int k = 20; // 执行多少次方模拟

    LL result = 1;   // Initialize result (base^0 = 1)
    map<LL, int> st; // Track positions of trailing digits
    int cycle_start = -1, cycle_length = -1;

    for (int i = 1; i <= k; i++) {
        result = (result * base) % mod; // Calculate trailing digits of base^i

        printf("%d^%2d = %40lld  trailing digits: %02lld",
               base, i, (LL)pow(base, i), result);

        if (st[result]) {
            cycle_start = st[result];
            cycle_length = i - cycle_start;
            printf(" \n\nCycle detected! Starts at %d, length = %d\n",
                   cycle_start, cycle_length);
            break;
        }
        st[result] = i;
        printf("\n");
    }

    if (cycle_length != -1) {
        cout << "\n============================\n";
        cout << "Simulation result: Trailing 2 digits cycle length = " << cycle_length << endl;
    }
    return 0;
}