# Solution of;
# Project Euler Problem 685: Inverse Digit Sum II
# https://projecteuler.net/problem=685
# 
# Writing down the numbers which have a digit sum of 10 in ascending order, we 
# get:$19, 28, 37, 46,55,64,73,82,91,109, 118,\dots$Let $f(n,m)$ be the 
# $m^{\text{th}}$ occurrence of the digit sum $n$. For example, $f(10,1)=19$, 
# $f(10,10)=109$ and $f(10,100)=1423$. Let $\displaystyle S(k)=\sum_{n=1}^k 
# f(n^3,n^4)$. For example $S(3)=7128$ and $S(10)\equiv 32287064 \mod 
# 1\,000\,000\,007$. Find $S(10\,000)$ 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 = 685
    timed.caller(dummy, n, i, prob_id)

# Solution of;
# Project Euler Problem 685: Inverse Digit Sum II
# https://projecteuler.net/problem=685
# 
# Writing down the numbers which have a digit sum of 10 in ascending order, we 
# get:$19, 28, 37, 46,55,64,73,82,91,109, 118,\dots$Let $f(n,m)$ be the 
# $m^{\text{th}}$ occurrence of the digit sum $n$. For example, $f(10,1)=19$, 
# $f(10,10)=109$ and $f(10,100)=1423$. Let $\displaystyle S(k)=\sum_{n=1}^k 
# f(n^3,n^4)$. For example $S(3)=7128$ and $S(10)\equiv 32287064 \mod 
# 1\,000\,000\,007$. Find $S(10\,000)$ 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 = 685
    timed.caller(dummy, n, i, prob_id)

# Solution of; # Project Euler Problem 685: Inverse Digit Sum II # https://projecteuler.net/problem=685 # # Writing down the numbers which have a digit sum of 10 in ascending order, we # get:$19, 28, 37, 46,55,64,73,82,91,109, 118,\dots$Let $f(n,m)$ be the # $m^{\text{th}}$ occurrence of the digit sum $n$. For example, $f(10,1)=19$, # $f(10,10)=109$ and $f(10,100)=1423$. Let $\displaystyle S(k)=\sum_{n=1}^k # f(n^3,n^4)$. For example $S(3)=7128$ and $S(10)\equiv 32287064 \mod # 1\,000\,000\,007$. Find $S(10\,000)$ modulo $1\,000\,000\,007$. # # by lcsm29 http://github.com/lcsm29/project-euler