vector<int> generate(int start, int end) {
    vector<bool> input(end+1, true);
    for (int i = 2; i * i<= end; ++i) {
        for (int j = i; i*j <= end    ; ++j) {
            input[i*j] = false;
        }
    }
    vector<int> primes;
    for (int i = start; i <= end; ++i) {
        if (input[i]) {
            primes.push_back(i);
        }
    }
    return primes;
}