# Question 5 – Divisible by K

## Divisible by K

Here, in this page we will discuss one of the problem Divisible by K that was asked in InfyTQ Advance Coding Section. We will discuss the problem description along with function description, Test Cases along with there explanation.

You will find the solution of the problem in different programming language.

## Problem Statement-:

Alice has a non-negative integer x written in the base y (a numeral system where 2 <= y <= 16). The number x has distinct digits. Bob has a number k written in the decimal numeral system. Alice wanted to check if the number x is divisible by the number k. However, Bob thinks it’s a very easy task. That’s why he proposed another problem: count the number of permutations of x which result in a number divisible by k.

Alice is confused and doesn’t know how to solve Bob’s problem, can you help her?

Notes:

1. y is given in decimal.
2. The possible digits for x start with the usual digits (0-9), and then with the letters (A – F), depending on the value of y. For example, if y = 12 then the digits are [0,1,… 9, A, B]. Also when y = 3, the possible digits are [0,1,2].
3.  Since x may contain letters, it’s inputted as a string.
4.  It’s guaranteed that the number x is a valid number in the base y, and that it doesn’t contain leading zeroes.
5. Since the final answer can be very large, output it modulo 1000000007 (10^9+7).

## Function Description:

Complete the divisible_k function in the editor below. It has the following parameter(s):

Parameters:

NameTypeDescription
yIntegerthe base which x is written in
kIntegerthe number which bob has
xStringAlice number written in the base y

Return: The function must return an INTEGER denoting the number of permutations of x which result in a number divisible by k.

## Constraints:

• 1 <= y <= 16
• 1 <= k <= 20
• 1 <= len(x) <= y

## Input Format for custom testing:

• The first line contains an integer, y, denoting the base which x is written in.
• The next line contains an integer, k, denoting the number which Bob has.
• The next line contains a string, x, denoting Alice’s number written in the base y.

## Sample Cases:

• Sample Input 1
5
4
24
• Sample Output 1
0
• Explanation
24 in base 5, is 14 in decimal. 42 in base 5, is 22 in decimal. For in both cases the number is not divisible by 4. So the answer is 0
`#include <bits/stdc++.h>using namespace std; int main(){    int y,k,m,ans=0;    string s;    cin>>y>>k>>s;    sort(s.begin(),s.end());    m=stoull(s,0,y);    if(m%k==0) ans++;    while(next_permutation(s.begin(),s.end()))    {        m=stoull(s,0,y);        if(m%k==0) ans++;    }    cout<<ans;}`
`from itertools import permutations y=int(input())k=int(input())s=input()ans=0p=permutations(s)L=set(p)pp=list(L)for i in list(pp):    a=''.join(i)    aa=int(a,y)    if aa%k==0:        ans+=1        print(ans)`