#include <bits/stdc++.h>
#include "paint.h"
using namespace std;
const int N = 2e5 + 30;
int n, k;
int pr[N];
bool dp[N][111], dp1[N][111];
bool col[N], cl[N];
int sm[N];
int qry(int l, int r)
{
if(l) return pr[r] - pr[l - 1];
return pr[r];
}
bool chk(int i1, int k1)
{
if(i1 >= 0) return dp[i1][k1];
return k1 == 0;
}
bool chk1(int i1, int k1)
{
if(i1 < n) return dp1[i1][k1];
return k1 == k;
}
string solve_puzzle(string s, vector<int> c)
{
n = s.length();
k = c.size();
for (int i = 0; i < n; i++)
{
pr[i] = (s[i] == '_');
if(i) pr[i] += pr[i - 1];
}
for (int i = 0; i < n; i++)
{
if(s[i] == 'X') break;
dp[i][0] = 1;
}
for (int i = 1; i <= k; i++)
{
for(int j = 0; j < n; j++)
{
if(c[i - 1] > j + 1) dp[j][i] = 0;
else if(qry(j - c[i - 1] + 1, j)) dp[j][i] = 0;
else if(j - c[i - 1] >= 0 && s[j - c[i - 1]] == 'X') dp[j][i] = 0;
else dp[j][i] = chk(j - c[i - 1] - 1, i - 1);
if(s[j] != 'X' && j) dp[j][i] = dp[j][i] | dp[j - 1][i];
}
}
for(int i = n - 1; i >= 0; i--)
{
if(s[i] == 'X') break;
dp1[i][k] = 1;
}
for(int i = k - 1; i >= 0; i--)
{
for(int j = n - 1; j >= 0; j--)
{
if(c[i] > n - j) dp1[j][i] = 0;
else if(qry(j, j + c[i] - 1)) dp1[j][i] = 0;
else if(j + c[i] < n && s[j + c[i]] == 'X') dp1[j][i] = 0;
else dp1[j][i] = chk1(j + c[i] + 1, i + 1);
if(s[j] != 'X') dp1[j][i] = dp1[j][i] | dp1[j + 1][i];
}
}
for (int i = 0; i < n; i++)
{
if(s[i] == 'X') continue;
for(int j = 0; j <= k; j++)
{
if(chk(i - 1, j) && chk1(i + 1, j)) cl[i] = 1;
}
}
for (int i = 0; i < k; i++)
{
int l = 0, r = c[i] - 1;
while(r < n)
{
bool bl = true;
if(qry(l, r)) bl = false;
else if(l && s[l - 1] == 'X') bl = false;
else if(r < n - 1 && s[r + 1] == 'X') bl = false;
else if(!chk(l - 2, i)) bl = false;
else if(!chk1(r + 2, i + 1)) bl = false;
if(bl) sm[l]++, sm[r + 1]--;
l++, r++;
}
}
for (int i = 0; i < n; i++)
{
if(i) sm[i] += sm[i - 1];
col[i] = sm[i];
}
for (int i = 0; i < n; i++)
{
if(s[i] != '.') continue;
if(col[i] && cl[i]) s[i] = '?';
else if(col[i]) s[i] = 'X';
else s[i] = '_';
}
return s;
}
