#pragma once
#include <bits/stdc++.h>
using namespace std;
#define forr(i, x , y) for(int i = x ; i<=y;i++)
#define fore(i , x) for(int i = 0 ; i<x;i++)
vector<vector<int>> pref;
auto compute_dp(int n , int K , string s , vector<int> c)
{
vector<vector<int>> dp(n + 1 , vector<int>(K + 1 , 0));
dp[0][0] = 1;
forr(i , 1 , n)
{
forr(j , 0 , K) {
if(j - 1 >= 0)
{
int l = i - c[j - 1] + 1;
int r = i;
if(l >= 1)
{
if(pref[0][r] - pref[0][l - 1] == 0)
{
if(j == 1)
{
dp[i][j]|=dp[i - c[j - 1]][j -1];
}
else
{
if(s[i - c[j - 1]] != 'X')
{
dp[i][j] |= dp[i - c[j - 1] - 1][j - 1];
}
}
}
}
}
if(s[i -1] != 'X')
dp[i][j]|=dp[i - 1][j];
}
}
return dp;
}
std::string solve_puzzle(std::string s, std::vector<int> c)
{
int n = (int)s.size();
int K = (int)c.size();
for(auto &C: s)
if(C == '.')C='?';
pref.assign(2 , vector<int>(n + 1 , 0));
forr(i , 1 , n)
{
pref[0][i] = pref[0][i - 1] + (s[i - 1] == '_');
pref[1][i] = pref[1][i - 1] + (s[i - 1] == 'X');
}
auto dpL = compute_dp(n , K, s , c);
reverse(s.begin() , s.end());
reverse(c.begin() , c.end());
auto dpR = compute_dp(n , K , s , c);
reverse(s.begin() , s.end());
reverse(c.begin() , c.end());
reverse(dpR.begin() , dpR.end());
for(auto &v : dpR)
reverse(v.begin() , v.end());
vector<int> can_black(n +2 , 0);
vector<int> val(n , 0);
forr(i , 1 , n)
{
if(s[i - 1] != 'X')
{
int cur = 0;
forr(k , 0 , K)
{
cur|=(dpL[i - 1][k] && dpR[i][k]);
}
if(cur == 1)
val[i-1]|=1;
}
}
forr(i , 1 , n)
{
if(s[i - 1] == '?' || s[i - 1] == 'X')
{
forr(k , 0 , K - 1)
{
int lt = i , rt = c[k] + i - 1;
if(rt > n)
continue;
bool checkL = ((i == 1) || s[i - 2] != 'X');
bool checkR = ((rt == n) || s[rt] != 'X');
int dpLeft ;
if(i <= 2)
dpLeft = (i <= 2 && k == 0);
else
dpLeft = dpL[i - 2][k];
int dpRight;
if(rt + 1 > n)
dpRight= (rt + 1 > n && (k + 1) == K);
else
dpRight = dpR[rt + 1][k + 1];
if(checkL && checkR && dpLeft && dpRight && ((pref[0][rt] - pref[0][i - 1]) == 0))
{
can_black[lt]++;
can_black[min(n + 1, rt + 1)]--;
}
}
}
}
forr(i , 1 , n)
{
can_black[i]+=can_black[i - 1];
if(can_black[i])
val[i - 1]|=2;
}
fore(i , n)
{
if(val[i] == 1)
s[i] = '_';
else if(val[i] == 2)
s[i] = 'X';
else
s[i] = '?';
}
return s;
}
