#include <cstdint>
#include <iostream>
#include <string>

namespace {

using i64 = std::int64_t;

struct Options {
    int n_max = 100;
    i64 threshold = 1000000;
    bool run_checkpoints = true;
};

bool parse_int_after_prefix(const std::string& arg, const std::string& prefix, int& value) {
    if (arg.rfind(prefix, 0U) != 0U) {
        return false;
    }
    const std::string tail = arg.substr(prefix.size());
    if (tail.empty()) {
        return false;
    }

    int parsed = 0;
    for (char c : tail) {
        if (c < '0' || c > '9') {
            return false;
        }
        parsed = parsed * 10 + static_cast<int>(c - '0');
    }
    value = parsed;
    return true;
}

bool parse_i64_after_prefix(const std::string& arg, const std::string& prefix, i64& value) {
    if (arg.rfind(prefix, 0U) != 0U) {
        return false;
    }
    const std::string tail = arg.substr(prefix.size());
    if (tail.empty()) {
        return false;
    }

    i64 parsed = 0;
    for (char c : tail) {
        if (c < '0' || c > '9') {
            return false;
        }
        parsed = parsed * 10 + static_cast<i64>(c - '0');
    }
    value = parsed;
    return true;
}

bool parse_arguments(int argc, char** argv, Options& options) {
    for (int i = 1; i < argc; ++i) {
        const std::string arg(argv[i]);
        if (arg == "--skip-checkpoints") {
            options.run_checkpoints = false;
            continue;
        }
        if (parse_int_after_prefix(arg, "--n-max=", options.n_max)) {
            continue;
        }
        if (parse_i64_after_prefix(arg, "--threshold=", options.threshold)) {
            continue;
        }

        std::cerr << "Unknown argument: " << arg << '\n';
        return false;
    }
    return options.n_max >= 1 && options.threshold >= 1;
}

int solve(const int n_max, const i64 threshold) {
    int count = 0;

    for (int n = 1; n <= n_max; ++n) {
        i64 c = 1;
        for (int r = 1; r <= n / 2; ++r) {
            c = (c * (n - r + 1)) / r;
            if (c > threshold) {
                count += (n + 1) - 2 * r;
                break;
            }
        }
    }

    return count;
}

bool run_checkpoints() {
    if (solve(10, 10) != 25) {
        std::cerr << "Checkpoint failed for n_max=10 threshold=10" << '\n';
        return false;
    }
    return true;
}

}  // namespace

int main(int argc, char** argv) {
    Options options;
    if (!parse_arguments(argc, argv, options)) {
        return 1;
    }
    if (options.run_checkpoints && !run_checkpoints()) {
        return 2;
    }

    std::cout << solve(options.n_max, options.threshold) << '\n';
    return 0;
}