This challenge is hard really hard

Question

i have to write a program which prints all unlucky numbers to N 1>N>10^13
where unlucky number is one that have 13 in it ex 139 or 513
and sum of it's digits is 13 ex 193 or 940
ex input 1000 output 2
ex input 123456 output 326

i have some code here, but it's slow for bigger numbers:

#include <iostream>
#include <string>

using namespace std;
bool sum_13(long n) {
long sum = 0;
while (n != 0) {
sum += n % 10;
n /= 10;
}
if(sum == 13) return 1;
else return 0;
}

bool isThirteen(long n) {

if(to_string(n).find("13") != string::npos) return 1;
return 0;
}

int isBadLuckNumber(long n) {
return isThirteen(n) && sum_13(n);
}

int badLuckNumbersToN(long n){
int cnt = 0;
for (size_t i = 0 ; i <= n; i++){
if (isBadLuckNumber(i)) cnt++;

}
return cnt;
}
long int n;
int main(){
cin >> n;
cout << badLuckNumbersToN(n);
cout << "\n";
return 0;
}

Answer 1

name due you require the solution in C only or can it be in python also?

Answer 2

c, c++ or python