// Time:  O(n * (logb + logc))
// Space: O(1)

// fast exponentiation
class Solution {
public:
    vector<int> getGoodIndices(vector<vector<int>>& variables, int target) {
        const auto& addmod = [&](uint32_t a, uint32_t b, uint32_t mod) {  // avoid overflow
            a %= mod, b %= mod;
            if (mod - a <= b) {
                b -= mod;  // relied on unsigned integer overflow in order to give the expected results
            }
            return a + b;
        };

        const auto& mulmod = [&](uint32_t a, uint32_t b, uint32_t mod)  {  // avoid overflow
            a %= mod, b %= mod;
            uint32_t result = 0;
            if (a < b) {
                swap(a, b);
            }
            while (b > 0)  { 
                if (b % 2 == 1) {
                    result = addmod(result, a, mod);
                }
                a = addmod(a, a, mod);
                b /= 2; 
            } 
            return result; 
        };

        const auto& powmod = [&](uint32_t a, uint32_t b, uint32_t mod) {
            a %= mod;
            uint32_t result = 1;
            while (b) {
                if (b & 1) {
                    result = mulmod(result, a, mod);
                }
                a = mulmod(a, a, mod);
                b >>= 1;
            }
            return result;
        };

        vector<int> result;
        for (int i = 0; i < size(variables); ++i) {
            if (powmod(powmod(variables[i][0], variables[i][1], 10), variables[i][2], variables[i][3]) == target) {
                result.emplace_back(i);
            }
        }
        return result;
    }
};