#include <algorithm>
#include <iostream>
#include "InfInt.h"

using namespace std;

template <typename Number >
Number Factorial(const Number& n)
{
  Number result = Number(1);

  for (Number i = Number(2); i <= n; ++i)
  {
    result *= i;
  }

  return result;
}

template <typename Number >
Number N_Choose_M(const Number& n, const Number& m)
{
  const Number result = Factorial(n) / Factorial(m) / Factorial(n - m);
  return result;
}

template <typename Number >
Number B(const Number& n, const Number& m)
{
  const Number maxK = n / m;

  Number sum = Number(0);

  for (Number k = Number(1); k <= maxK; ++k)
  {
    Number product = Number(1);
    for (Number j = Number(0); j < m; ++j)
    {
      const Number c = N_Choose_M(n - (k*j), k);
      product *= c;
    }

    sum += product;
  }

  const Number factorial = Factorial(m);
  const Number result = sum / factorial;
  return result;
}

template <typename Number >
Number C(const Number& n)
{
  const Number minM = Number(2);

  Number result = Number(0);

  for (Number m = minM; m <= n; ++m)
  {
    const Number b = B(n, m);
    result += b;
  }

  return result;
}

template <typename Number >
void PrintValuesOfB(const Number& m, const Number& count)
{
  const Number maxN = m + count;

  for (Number n = m; n <= maxN; ++n)
  {
    const Number b = B(n, m);

    int printLatex = 0;
    if (printLatex)
    {
      cout << "\\{{\\keyw " << n << "},{\\num " << b << "}\\}; " << endl;
    }
    else
    {
      cout << "b(" << n << ", " << m << ")=" << b << endl;
    }
  }
}

template <typename Number >
void PrintValuesOfC(const Number& initialN, const Number& count)
{
  const Number maxN = initialN + count;

  for (Number n = initialN; n <= maxN; ++n)
  {
    const Number b = C(n);

    int printLatex = 0;
    if (printLatex)
    {
      cout << "\\{{\\keyw " << n << "},{\\num " << b << "}\\}; " << endl;
    }
    else
    {
      cout << n << " " << b << endl;
    }
  }
}

int main()
{
  try
  {
    typedef InfInt Number;

    const Number count = 200;
    const Number initialValue = 2;

    int printB = 0;
    if (printB)
    {
      PrintValuesOfB(initialValue, count);
    }
    else
    {
      PrintValuesOfC(initialValue, count);
    }
  }
  catch (exception& ex)
  {
    cout << "Error: " << ex.what() << endl;

    return 1;
  }
  catch (...)
  {
    cout << "Unknown error." << endl;
    return 2;
  }

  return 0;
}