#!/bin/bash
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
# Copyright (C) 2008 Vino Fernando Crescini  <vfcrescini@gmail.com>

# Google Treasure Hunt 2008 Puzzle 1

function is_num
{
  tmp=${1//[0-9]/}

  if [ "$tmp" != "" ]; then
    return 1
  fi

  return 0
}

if [ $# -ne 2 ]; then
  echo "usage: $0 <m> <n>"
  exit 1
fi

if ! is_num $1 || ! is_num $2; then
  echo "m and n must be positive integers"
  exit 2
fi

bc -q <<EOF
  define f(x)
  {
    if (x <= 1)
      return(1);

    return (x * f(x - 1));
  }

  define pas(n, k)
  {
    return (f(n) / (f(k) * f(n - k)));
  }

  define solve(g1, g2)
  {
    n = (g1 + g2 - 2);
    k = (g1 - 1);

    return(pas(n, k));
  }

  solve($1, $2);
  halt;
EOF

exit $?