#!/usr/bin/env python3
########################################################################
# Solves problem 207 from projectEuler.net.
# Finds the smallest M for which P(m) < 1/12345
# Copyright (C) 2011 Santiago Alessandri
#
# 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 .
#
# You can contact me at san.lt.ss@gmail.com
# Visit my wiki at http://san-ss.wikidot.com
########################################################################
from fractions import Fraction
from math import log
calc_k = lambda x: x * (x - 1)
cant_perf = 1
cant_tot = 1
limit = Fraction(1, 12345)
if __name__ == '__main__':
i = 3
while Fraction(cant_perf, cant_tot) >= limit:
log_2 = int(log(i,2))
if 2 ** log_2 == i:
cant_perf += 1
cant_tot += 1
i += 1
i -= 1
print("The result is:", calc_k(i))