This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define int long long
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
char c[501][501];
int n, m;
void init(){
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
if((i == n - 1) == (j == m - 1)) c[i][j] = '.';
else if(i == n - 1) c[i][j] = 'r';
else c[i][j] = 'd';
}
}
}
void output(){
cout << n << ' ' << m << endl;
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
cout << c[i][j];
}
cout << endl;
}
}
ostream& operator<< (ostream& out, __int128_t x){
string s; while(x > 0) s.push_back('0' + (x % 10)), x /= 10; reverse(s.begin(), s.end());
return out << s;
}
__int128_t dp[501][501][2];
__int128_t C[501][501];
void revert(int i, int j){
if(c[i][j] == 'X'){
dp[i][j + 1][0] -= dp[i][j][0] + dp[i][j][1];
dp[i + 1][j][1] -= dp[i][j][0] + dp[i][j][1];
}else if(c[i][j] == 'r'){
dp[i][j + 1][0] -= dp[i][j][0] + dp[i][j][1];
}else if(c[i][j] == 'd'){
dp[i + 1][j][1] -= dp[i][j][0] + dp[i][j][1];
}else{
if(j + 1 < m) dp[i][j + 1][0] -= dp[i][j][0];
if(i + 1 < n) dp[i + 1][j][1] -= dp[i][j][1];
}
}
void update(int i, int j){
if(c[i][j] == 'X'){
dp[i][j + 1][0] += dp[i][j][0] + dp[i][j][1];
dp[i + 1][j][1] += dp[i][j][0] + dp[i][j][1];
}else if(c[i][j] == 'r'){
dp[i][j + 1][0] += dp[i][j][0] + dp[i][j][1];
}else if(c[i][j] == 'd'){
dp[i + 1][j][1] += dp[i][j][0] + dp[i][j][1];
}else{
if(j + 1 < m) dp[i][j + 1][0] += dp[i][j][0];
if(i + 1 < n) dp[i + 1][j][1] += dp[i][j][1];
}
}
__int128_t get(int i, int j){
return dp[i][j][0] + dp[i][j][1];
}
__int128_t calc(){
int N = n, M = m;
memset(dp, 0, sizeof(dp));
dp[0][0][0] = 1; dp[0][0][1] = 0;
for(int i = 0; i < N; i++){
for(int j = 0; j < M; j++){
update(i, j);
}
}
return dp[N - 1][M - 1][0] + dp[N - 1][M - 1][1];
}
void part2(int K){
n = m = 49;
for(int L = 1; L <= 26; L++){
for(int round = 0; round < 100; round++){
init();
for(int i = 0; i < L; i++){
for(int j = 0; j < m - 1; j++){
c[i][j] = rng() % 10 ? 'X' : '.';
}
}
int cur = calc(); if(cur > K) continue;
for(int i = L; i < n; i++){
for(int j = m - 2; j >= 0; j--){
c[i][j] = 'X';
if(calc() > K){
c[i][j] = '.';
}
}
}
if(calc() == K){
output();
return;
}
}
}
}
int32_t main(){
int K; cin >> K;
part2(K);
}
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