#include <bits/stdc++.h>
using namespace std;
typedef int64_t ll;
typedef long long ll;
typedef pair<ll,ll> lll;
typedef pair<ll,int> lli;
typedef pair<int,int> pii;
#define EL printf("\n")
#define OK printf("OK")
#define pb push_back
#define mp make_pair
#define ep emplace_back
#define X first
#define Y second
#define fillchar(a,x) memset(a, x, sizeof(a))
#define FOR(i,l,r) for (int i=l;i<=r;i++)
#define FORD(i,r,l) for (int i=r;i>=l;i--)
#define sz(v) (int)v.size()
const int base = 1e9;
typedef vector<int> BigInt;
void Set(BigInt &a) {
while (a.size() > 1 && a.back() == 0) a.pop_back();
}
void Print(BigInt a) {
Set(a);
printf("%d", (a.size() == 0) ? 0 : a.back());
FORD(i,a.size()-2,0) printf("%09d", a[i]); EL;
}
BigInt Integer(string s) {
BigInt ans;
if (s[0] == '-') return ans;
if (s.size() == 0) {ans.pb(0); return ans;}
while (s.size()%9 != 0) s = '0'+s;
for (int i=0;i<(int)s.size();i+=9) {
int v = 0;
for (int j=i;j<i+9;j++) v = v*10+(s[j]-'0');
ans.insert(ans.begin(),v);
}
Set(ans);
return ans;
}
BigInt Integer(char c[]) {
string s = "";
FOR(i,0,(int)strlen(c)-1) s = s + c[i];
return Integer(s);
}
BigInt Integer(ll x) {
string s = "";
while (x > 0) s = char(x%10+'0') + s, x /= 10;
return Integer(s);
}
BigInt Integer(int x) {
return Integer((ll) x);
}
void operator >> (istream &in, BigInt &a) {
string s;
cin >> s;
a = Integer(s);
}
void operator << (ostream &out, BigInt a) {
Print(a);
}
bool operator < (BigInt a, BigInt b) {
Set(a);
Set(b);
if (a.size() != b.size()) return (a.size() < b.size());
FORD(i,a.size()-1,0)
if (a[i] != b[i]) return (a[i] < b[i]);
return false;
}
bool operator > (BigInt a, BigInt b) {
return (b < a);
}
bool operator == (BigInt a, BigInt b) {
return (!(a < b) && !(b < a));
}
bool operator <= (BigInt a, BigInt b) {
return (a < b || a == b);
}
bool operator >= (BigInt a, BigInt b) {
return (b < a || b == a);
}
bool operator < (BigInt a, int b) {
return (a < Integer(b));
}
bool operator > (BigInt a, int b) {
return (a > Integer(b));
}
bool operator == (BigInt a, int b) {
return (a == Integer(b));
}
bool operator >= (BigInt a, int b) {
return (a >= Integer(b));
}
bool operator <= (BigInt a, int b) {
return (a <= Integer(b));
}
BigInt max(BigInt a, BigInt b) {
if (a > b) return a;
return b;
}
BigInt min(BigInt a, BigInt b) {
if (a < b) return a;
return b;
}
BigInt operator + (BigInt a, BigInt b) {
Set(a);
Set(b);
BigInt ans;
int carry = 0;
FOR(i,0,max((int)a.size(), (int)b.size())-1) {
if (i < (int)a.size()) carry += a[i];
if (i < (int)b.size()) carry += b[i];
ans.pb(carry%base);
carry /= base;
}
if (carry) ans.pb(carry);
Set(ans);
return ans;
}
BigInt operator + (BigInt a, int b) {
return a + Integer(b);
}
BigInt operator ++ (BigInt &a) { // ++a
a = a + 1;
return a;
}
void operator += (BigInt &a, BigInt b) {
a = a + b;
}
void operator += (BigInt &a, int b) {
a = a + b;
}
BigInt operator - (BigInt a, BigInt b) {
Set(a);
Set(b);
BigInt ans;
int carry = 0;
FOR(i,0,(int)a.size()-1) {
carry += a[i] - (i < (int)b.size() ? b[i] : 0);
if (carry < 0) ans.pb(carry+base), carry = -1;
else ans.pb(carry), carry = 0;
}
Set(ans);
return ans;
}
BigInt operator - (BigInt a, int b) {
return a - Integer(b);
}
void operator -- (BigInt &a) { // --a
a = a - 1;
}
void operator -= (BigInt &a, BigInt b) {
a = a - b;
}
void operator -= (BigInt &a, int b) {
a = a - b;
}
BigInt operator * (BigInt a, BigInt b) {
Set(a);
Set(b);
BigInt ans;
ans.assign(a.size()+b.size(), 0);
FOR(i,0,(int)a.size()-1) {
ll carry = 0ll;
for (int j=0;j<(int)b.size() || carry > 0;j++) {
ll s = ans[i+j] + carry + (ll)a[i]*(j<(int)b.size()?(ll)b[j]:0ll);
ans[i+j] = s%base;
carry = s/base;
}
}
Set(ans);
return ans;
}
BigInt operator * (BigInt a, int b) {
return a * Integer(b);
}
void operator *= (BigInt &a, BigInt b) {
a = a * b;
}
void operator *= (BigInt &a, int b) {
a = a * b;
}
BigInt operator / (BigInt a, BigInt b) {
Set(a);
Set(b);
if (b == Integer(0)) return Integer("-1");
BigInt ans, cur;
FORD(i,a.size()-1,0) {
cur.insert(cur.begin(), a[i]);
int x = 0, L = 0, R = base;
while (L <= R) {
int mid = (L+R)>>1;
if (b*Integer(mid) > cur) {
x = mid;
R = mid-1;
}
else
L = mid+1;
}
cur = cur - Integer(x-1)*b;
ans.insert(ans.begin(),x-1);
}
Set(ans);
return ans;
}
BigInt operator / (BigInt a, int b) {
Set(a);
BigInt ans;
ll cur = 0ll;
FORD(i,a.size()-1,0) {
cur = (cur*(ll)base + (ll)a[i]);
ans.insert(ans.begin(),cur/b);
cur %= b;
}
Set(ans);
return ans;
}
void operator /= (BigInt &a, BigInt b) {
a = a / b;
}
void operator /= (BigInt &a, int b) {
a = a / b;
}
BigInt operator % (BigInt a, BigInt b) {
Set(a);
Set(b);
if (b == Integer(0)) return Integer("-1");
BigInt ans;
FORD(i,a.size()-1,0) {
ans.insert(ans.begin(), a[i]);
int x = 0, L = 0, R = base;
while (L <= R) {
int mid = (L+R)>>1;
if (b*Integer(mid) > ans) {
x = mid;
R = mid-1;
}
else
L = mid+1;
}
ans = ans - Integer(x-1)*b;
}
Set(ans);
return ans;
}
int operator % (BigInt a, int b) {
Set(a);
if (b == 0) return -1;
int ans = 0;
FORD(i,a.size()-1,0)
ans = (ans*(base%b) + a[i]%b)%b;
return ans;
}
void operator %= (BigInt &a, BigInt b) {
a = a % b;
}
void operator %= (BigInt &a, int b) {
a = a % Integer(b);
}
BigInt gcd(BigInt a, BigInt b) {
Set(a);
Set(b);
while (b > Integer(0)) {
BigInt r = a%b;
a = b;
b = r;
}
Set(a);
return a;
}
BigInt lcm(BigInt a, BigInt b) {
return (a*b/gcd(a,b));
}
BigInt sqrt(BigInt a) {
BigInt x0 = a, x1 = (a+1)/2;
while (x1 < x0) {
x0 = x1;
x1 = (x1+a/x1)/2;
}
return x0;
}
BigInt pow(BigInt a, BigInt b) {
if (b == Integer(0)) return Integer(1);
BigInt tmp = pow(a, b/2);
if (b%2 == 0) return tmp * tmp;
return tmp * tmp * a;
}
BigInt pow(BigInt a, int b) {
return pow(a,(Integer(b)));
}
int log(int n, BigInt a) { // log_n(a)
Set(a);
int ans = 0;
while (a > Integer(1)) {
ans++;
a /= n;
}
return ans;
}
bool isEligible(int x, int y, int n, int m){
return x >= 0 && x < n && y >= 0 && y < m;
}
BigInt fact[60];
int main(){
fact[0] = Integer(1);
for(int i = 1; i < 60; i++){
fact[i] = fact[i-1]*i;
}
ll n, m;
string s = "";
BigInt k;
cin >> n;
cin >> m;
char grid[n][m];
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
cin >> grid[i][j];
}
}
cin >> k;
queue <pii> K;
K.push(mp(0, 0));
while(sz(K)){
while(sz(K)){
auto v = K.front(); K.pop();
vector <pii> vec;
vec.pb(v);
while(sz(K) && grid[K.front().first][K.front().second] == grid[v.first][v.second]){
vec.pb(K.front());
K.pop();
}
BigInt tmp = Integer(0);
for(auto to : vec){
BigInt tmp2 = fact[(n-to.first)+(m-to.second)-2]/fact[(n-to.first)-1]/fact[((n-to.first)+(m-to.second)-2)-(n-to.first-1)];
if(isEligible(to.first-1, to.second, n, m) && isEligible(to.first, to.second-1, n, m) &&
grid[to.first-1][to.second] == grid[to.first][to.second-1]) tmp2 *= 2;
tmp += tmp2;
}
if(k <= tmp){
s += grid[v.first][v.second];
tmp = Integer(0);
for(auto to : vec){
BigInt tmp2 = fact[(n-to.first)+(m-to.second)-2]/fact[(n-to.first)-1]/fact[((n-to.first)+(m-to.second)-2)-(n-to.first-1)];
if(isEligible(to.first-1, to.second, n, m) && isEligible(to.first, to.second-1, n, m) &&
grid[to.first-1][to.second] == grid[to.first][to.second-1]) tmp += tmp2;
}
if(tmp <= k) k -= tmp;
set <pair <char, pii>> st;
for(auto to : vec){
if(isEligible(to.first, to.second+1, n, m)) st.insert(mp(grid[to.first][to.second+1], mp(to.first, to.second+1)));
if(isEligible(to.first+1, to.second, n, m)) st.insert(mp(grid[to.first+1][to.second], mp(to.first+1, to.second)));
}
while(sz(K)) K.pop();
for(auto to : st) K.push(to.second);
break;
}
else{
k -= tmp;
}
}
}
cout << s << endl;
return 0;
}
/*
4 5
abcdz
bcdif
adzab
dzdtc
11
*/
Compilation message
kthpath.cpp:6:19: error: conflicting declaration 'typedef long long int ll'
6 | typedef long long ll;
| ^~
kthpath.cpp:5:17: note: previous declaration as 'typedef int64_t ll'
5 | typedef int64_t ll;
| ^~
kthpath.cpp: In function 'BigInt operator/(BigInt, BigInt)':
kthpath.cpp:247:41: warning: ISO C++ forbids converting a string constant to 'char*' [-Wwrite-strings]
247 | if (b == Integer(0)) return Integer("-1");
| ^~~~
kthpath.cpp: In function 'BigInt operator%(BigInt, BigInt)':
kthpath.cpp:294:41: warning: ISO C++ forbids converting a string constant to 'char*' [-Wwrite-strings]
294 | if (b == Integer(0)) return Integer("-1");
| ^~~~
