#include "paint.h"
#include "bits/stdc++.h"
using namespace std;
string solve_puzzle(string s, vector<int> c) {
int n = s.size(), k = c.size();
s = "$" + s + "$";
vector<int> white(n+2, 0), black(n+2, 0);
for (int i = 1; i <= n+1; i++){
white[i] = white[i-1] + (s[i] == '_');
black[i] = black[i-1] + (s[i] == 'X');
}
reverse(c.begin(), c.end());
c.push_back(-1);
reverse(c.begin(), c.end());
vector<vector<bool> > pref(n+3, vector<bool>(k+2, 0));
vector<vector<bool> > suf(n+3, vector<bool>(k+2, 0));
for (int i = 0; i <= n+2; i++){
pref[i][0] = black[i] == 0;
suf[i][k+1] = black[n] == black[i - 1];
}
for (int i = 1; i <= n; i++)
for (int j = 1; j <= k; j++){
if (s[i] != 'X')
pref[i][j] = pref[i-1][j];
if (i >= c[j] and white[i] == white[i-c[j]]){
if (i == c[j]){
if (j == 1)
pref[i][j] = true;
}
else if (s[i-c[j]] != 'X')
pref[i][j] = pref[i][j] | pref[i-c[j]-1][j-1];
}
}
for (int i = n; i >= 1; i--)
for (int j = 1; j <= k; j++){
if (s[i] != 'X')
suf[i][j] = suf[i+1][j];
if (i + c[j] <= n+1 and white[i+c[j]-1] == white[i-1] and s[i+c[j]] != 'X')
suf[i][j] = suf[i][j] | suf[i+c[j]+1][j+1];
}
//put white
vector<int> answer(n+1, 0);
for (int i = 1; i <= n; i++)
if (s[i] == '.'){
for (int j = 1; j <= k+1; j++)
if (pref[i-1][j-1] and suf[i+1][j]){
answer[i] |= 1;
break;
}
}
//put black
for (int j = 1; j <= k; j++)
for (int i = 1; i + c[j] <= n+1; i++){
int l = i, r = i + c[j] - 1;
if (white[r] == white[l-1] and s[l-1] != 'X' and s[r+1] != 'X'){
if (l==1){
if (suf[r+2][j+1]){
for (int h = l; h <= r; h++)
answer[h] |= 2;
}
}
else if(pref[l-2][j-1] and suf[r+2][j+1]){
for (int h = l; h <= r; h++)
answer[h] |= 2;
}
}
}
string result;
for (int i = 1; i <= n; i++){
if (s[i] == '.'){
if (answer[i] == 1)
result += '_';
else if(answer[i] == 2)
result += 'X';
else
result += '?';
}
else
result += s[i];
}
return result;
}
