#include<bits/stdc++.h>
using namespace std;


string xor1(string a, string b)
{


string result = "";

int n = b.length();


for(int i = 1; i < n; i++)
{
if (a[i] == b[i])
result += "0";
else
result += "1";
}
return result;
}


string mod2div(string divident, string divisor)
{


int pick = divisor.length();



string tmp = divident.substr(0, pick);

int n = divident.length();

while (pick < n)
{
if (tmp[0] == '1')


tmp = xor1(divisor, tmp) + divident[pick];
else


tmp = xor1(std::string(pick, '0'), tmp) +
divident[pick];

pick += 1;
}


if (tmp[0] == '1')
tmp = xor1(divisor, tmp);
else
tmp = xor1(std::string(pick, '0'), tmp);

return tmp;
}


void encodeData(string data, string key)
{
int l_key = key.length();


string appended_data = (data +
std::string(
l_key - 1, '0'));

string remainder = mod2div(appended_data, key);


string codeword = data + remainder;
cout << "Remainder : "
<< remainder << "\n";
cout << "Encoded Data (Data + Remainder) :"
<< codeword << "\n";
}

int main()
{
string data = "100100";
string key = "1101";

encodeData(data, key);

return 0;
}