#include "paint.h"
#include <bits/stdc++.h>
#define N 200005
#define K 105
using namespace std;
int prew[N];
int preb[N];
bool predp[N][K];
bool sufdp[N][K];
int canb[N];
int cntw(int l,int r){
return prew[r] - prew[l-1];
}
int cntb(int l,int r){
return preb[r] - preb[l-1];
}
string solve_puzzle(string s, vector<int> c) {
for(auto &u:s)if(u == '.')u = '?';
s = "#" + s + "_";
int n = s.size() - 1;
int k = c.size();
for(int i = 1;i<=n;i++){
prew[i] = prew[i-1] + (s[i] == '_');
preb[i] = preb[i-1] + (s[i] == 'X');
}
predp[0][0] = 1;
for(int i = 1;i<=n;i++){
for(int j = 0;j<=k;j++){
if(s[i] != 'X'){
predp[i][j] |= predp[i-1][j];
}
}
for(int j = 1;j<=k;j++){
if(i + c[j-1] <= n && cntw(i,i+c[j-1]-1) == 0 && cntb(i+c[j-1],i+c[j-1]) == 0){
predp[i+c[j-1]][j] |= predp[i-1][j-1];
}
}
}
sufdp[n+1][k+1] = 1;
for(int i = n;i>=1;i--){
for(int j = 1;j<=k+1;j++){
if(s[i] != 'X'){
sufdp[i][j] |= sufdp[i+1][j];
}
}
for(int j = 1;j<=k;j++){
if(i - c[j-1] >= 1 && cntw(i-c[j-1],i-1) == 0 && cntb(i,i) == 0){
sufdp[i-c[j-1]][j] |= sufdp[i+1][j+1];
}
}
}
for(int i = 1;i<=n;i++){
for(int j = 1;j<=k;j++){
if(i + c[j-1] <= n && cntw(i,i+c[j-1]-1) == 0 && cntb(i+c[j-1],i+c[j-1]) == 0 && predp[i-1][j-1] && sufdp[i+c[j-1]+1][j+1]){
canb[i] += 1;
canb[i + c[j-1]] -= 1;
}
}
}
for(int i = 1;i<=n;i++){
canb[i] += canb[i-1];
}
string ans = "";
for(int i = 1;i<n;i++){
if(s[i] != '?'){
ans += s[i];
continue;
}
bool canw = 0;
for(int j = 0;j<=k;j++){
canw |= predp[i][j] && sufdp[i+1][j+1];
}
if(canb[i] && canw)ans += "?";
else if(canb[i])ans += "X";
else if(canw)ans += '_';
else assert(0);
}
return ans;
}
