KEK

#include <iostream>
#include <vector>
#include <cmath>

long long rectangle_rotation(int a, int b)
{

    // TODO: fix mistakes while calculating big coords

    std::cout << a << '\t' << b << '\n';

    std::vector<std::pair<double, double>> coords;

    coords.emplace_back(-a/2*cos(M_PI/4) - b/2*sin(M_PI/4), -a/2*sin(M_PI/4) + b/2*cos(M_PI/4));
    coords.emplace_back(-a/2*cos(M_PI/4) + b/2*sin(M_PI/4), -a/2*sin(M_PI/4) - b/2*cos(M_PI/4));
    coords.emplace_back((-1)*(coords[0].first), (-1)*(coords[0].second));
    coords.emplace_back((-1)*(coords[1].first), (-1)*(coords[1].second));

    for (auto& i : coords)
        std::cout << i.first << '\t' << i.second << '\n';

    double left_edge = coords[0].first;
    double right_edge = -1*left_edge;
    double subEdgeLeft = (a > b) ? coords.at(1).first : coords.at(3).first;
    double subEdgeRight = (a > b) ? coords.at(3).first : coords.at(1).first;

    double b03 = coords.at(3).second - coords.at(3).first;
    double b01 = coords.at(0).second + coords.at(0).first;
    double b32 = -b01;
    double b12 = -b03;

    long long counter {0};

    int initX = static_cast<int>(floor(left_edge + 1));

    for (; initX <= subEdgeLeft; initX += 1)
        for (auto coordY = static_cast<int>(floor(initX + b03)); coordY >= -initX + b01; coordY -= 1)
            counter++;
    if (a > b)
    {
        for (; initX <= subEdgeRight; initX += 1)
            for (auto coordY = static_cast<long>(floor(initX + b03)); coordY >= initX + b12; coordY -= 1)
                counter++;
        for (; initX <= right_edge; initX += 1)
            for (auto coordY = static_cast<long>(floor(-initX + b32)); coordY >= initX + b12; coordY -= 1)
                counter++;
    }
    else
    {
        for (; initX <= subEdgeRight; initX += 1)
            for (auto coordY = static_cast<long>(floor(-initX + b32)); coordY >= -initX + b01; coordY -= 1)
                counter++;
        for (; initX <= right_edge; initX += 1)
            for (auto coordY = static_cast<long>(floor(-initX + b32)); coordY >= initX + b12; coordY -= 1)
                counter++;
    }

    return counter; // Do your magic!
}

int main()
{
    rectangle_rotation(3706,6632);
    return 0;
}