/* Author : Mohamed Ahmed Bakry (handle : MohamedAhmed04)
contest name : International Olympiad in informatics (IOI) 2016 day 2
problem name : Paint By Numbers (IOI 2016-Paint)
problem link : https://oj.uz/problem/view/IOI16_paint
problem's solution :
I think it's same like editorial idea :
https://github.com/mostafa-saad/MyCompetitiveProgramming/blob/master/Olympiad/IOI/official/2016/ioi2016solutions.pdf
*/
//#include "grader.cpp"
#include "paint.h"
#include <bits/stdc++.h>
using namespace std ;
std::string solve_puzzle(std::string s, std::vector<int> c)
{
int n = s.size() , m = c.size() ;
int arr[n+5] , pref[n+5] ;
pref[0] = 0 ;
for(int i = 1 ; i <= n ; ++i)
{
if(s[i-1] == 'X')
arr[i] = 1 ;
else if(s[i-1] == '_')
arr[i] = 0 ;
else if(s[i-1] == '.')
arr[i] = -1 ;
pref[i] = pref[i-1] ;
if(arr[i] == 0)
pref[i]++ ;
}
int dp1[n+2][m+2][3] ;
memset(dp1 , 0 , sizeof(dp1)) ;
dp1[0][0][0] = 1 ;
for(int i = 1 ; i <= n ; ++i)
{
for(int j = 0 ; j <= m ; ++j)
{
for(int k = 0 ; k <= 1 ; ++k)
{
if(arr[i] != -1 && arr[i] != k)
continue ;
if(k == 0)
{
dp1[i][j][k] = dp1[i-1][j][k] ;
if(j > 0)
{
if(i-c[j-1] >= 1)
dp1[i][j][k] |= dp1[i-c[j-1]][j-1][1] ;
}
}
else if(k == 1 && j != m)
{
if(i+c[j]-1 <= n && pref[i+c[j]-1] - pref[i-1] == 0)
dp1[i][j][k] = dp1[i-1][j][0] ;
}
}
}
}
int dp2[n+2][m+2][3] ;
memset(dp2 , 0 , sizeof(dp2)) ;
dp2[n+1][m][0] = 1 ;
for(int i = n ; i >= 1 ; --i)
{
for(int j = 0 ; j <= m ; ++j)
{
for(int k = 0 ; k <= 1 ; ++k)
{
if(arr[i] != -1 && arr[i] != k)
continue ;
if(k == 0)
{
dp2[i][j][k] = dp2[i+1][j][k] ;
dp2[i][j][k] |= dp2[i+1][j][1] ;
}
else if(k == 1 && j != m)
{
if(i+c[j]-1 <= n && pref[i+c[j]-1] - pref[i-1] == 0)
{
dp2[i][j][k] = dp2[i+c[j]][j+1][0] ;
}
}
}
}
}
string ans = "" ;
int Max = -1 ;
for(int i = 1 ; i <= n ; ++i)
{
for(int j = 0 ; j < m ; ++j)
{
if(dp1[i][j][1] == 1 && dp2[i][j][1] == 1)
Max = max(Max , i+c[j]-1) ;
}
if(arr[i] == 1)
ans.push_back('X') ;
else if(arr[i] == 0)
ans.push_back('_') ;
else if(arr[i] == -1)
{
bool flag1 = false , flag2 = false ;
for(int j = 0 ; j <= m ; ++j)
{
if(dp1[i][j][0] == 1 && dp2[i][j][0] == 1)
flag1 = true ;
}
if(Max >= i)
flag2 = true ;
if(flag1 == 1 && flag2 == 1)
ans.push_back('?');
else if(flag1 == 1)
ans.push_back('_') ;
else if(flag2 == 1)
ans.push_back('X') ;
}
}
return ans ;
}
