#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
class NextHomogeneousStrings { public:
string getNext(int d, int n, string seed, long long k)
{
int M = seed.size();
LL L=0, R=1; // [L,R)
while( R-L > 2 ) {
LL C = (R+L)/2;
string t = xth(d,n,C,M);
(t=="" || seed<t ? R : L) = C;
}
return seed==xth(d,n,L,M) ? xth(d,n,L+k-1,M) : xth(d,n,L+k,M);
}
string xth(int d, int n, LL x, int M)
{
return rec( string(), x, d, n, M );
}
string rec( string hist, LL x, int d, int n, int M )
{
if( M == 0 )
return "";
for(char c='a'; c<='z'; ++c)
{
string hh = hist + c;
// todo: normalize
if( x < cnt(hh,d,n,M) )
return c + rec(hist+c, x, d, n, M-1);
x -= cnt(hh,d,n,M);
}
return "";
}
LL cnt(string hist, int d, int n, int M)
{
if( M == 0 )
return 1;
// todo: memoize
LL ans = 0;
for(char c='a'; c<='z'; ++c)
{
char cc = c;
if( find(hist.begin(), hist.end(), c)==hist.end() )
cc = *max_element(hist.begin(),hist.end()) + 1; // todo: end then 'a'
string h2 = hist+cc;
// todo: check violation
// todo: drop 1st (if needed)
// todo: normalize
//ans += cnt(h2, dd, nn, M-1);
}
return ans;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const string& Expected, const string& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, NextHomogeneousStrings().getNext(d, n, seed, k));}
int main(){
CASE(0)
int d = 1;
int n = 2;
string seed = "aaa";
long long k = 3LL;
string _ = "ddd";
END
CASE(1)
int d = 2;
int n = 3;
string seed = "abc";
long long k = 0LL;
string _ = "aca";
END
CASE(2)
int d = 2;
int n = 4;
string seed = "ttrrzz";
long long k = 6LL;
string _ = "ttsssc";
END
CASE(3)
int d = 6;
int n = 8;
string seed = "txyaaxaassaaaarghjsdohasdghususdidisisdodo";
long long k = 10000000000000000LL;
string _ = "txyaaxaassaaaarghjsgaaaaaaaaadntffiniqrddy";
END
CASE(4)
int d = 2;
int n = 5;
string seed = "zzzzzaa";
long long k = 100LL;
string _ = "";
END
/*
CASE(5)
int d = ;
int n = ;
string seed = ;
long long k = LL;
string _ = ;
END
CASE(6)
int d = ;
int n = ;
string seed = ;
long long k = LL;
string _ = ;
END
*/
}
// END CUT HERE