string maxSegmentArea(vector<int>& radii, int requiredSegments) {
    sort(radii.begin(), radii.end());

    const float PI = 3.14159265359f;
    int largestRadius = radii.back();
    float minArea = 0.0f;
    float maxArea = largestRadius * largestRadius * 1.0f;

    float bestArea = 0.0f;
    int iterationCount = 0;

    while (maxArea - minArea > 1e-5 && iterationCount <= 10000000) {
        float currentTargetArea = (minArea + maxArea) / 2.0f;

        int segmentsFormed = 0;
        bool enoughSegments = false;

        for (int i = radii.size() - 1; i >= 0; i--) {
            float circleArea = radii[i] * radii[i] * 1.0f;
            segmentsFormed += floor(circleArea / currentTargetArea);

            if (segmentsFormed >= requiredSegments) {
                enoughSegments = true;
                break;
            }
        }

        if (enoughSegments) {
            bestArea = max(bestArea, currentTargetArea);
            minArea = currentTargetArea + 1e-6f;
        } else {
            maxArea = currentTargetArea - 1e-6f;
        }

        iterationCount++;
    }

    // Multiply by PI only once at the end
    bestArea *= PI;

    // Round to 4 decimal places
    float roundedArea = round(bestArea * 10000.0f) / 10000.0f;
    ostringstream out;
    out << fixed << setprecision(4) << roundedArea;
    return out.str();
}