# Solution of;
# Project Euler Problem 688: Piles of Plates
# https://projecteuler.net/problem=688
# 
# We stack $n$ plates into $k$ non-empty piles where each pile is a different 
# size. Define $f(n,k)$ to be the maximum number of plates possible in the 
# smallest pile. For example when $n = 10$ and $k = 3$ the piles $2,3,5$ is 
# the best that can be done and so $f(10,3) = 2$. It is impossible to divide 
# 10 into 5 non-empty differently-sized piles and hence $f(10,5) = 0$. Define 
# $F(n)$ to be the sum of $f(n,k)$ for all possible pile sizes $k\ge 1$. For 
# example $F(100) = 275$. Further define $S(N) = \displaystyle\sum_{n=1}^N 
# F(n)$. You are given $S(100) = 12656$. Find $S(10^{16})$ giving your answer 
# modulo $1\,000\,000\,007$.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 688
    timed.caller(dummy, n, i, prob_id)
