#include <bits/stdc++.h>
#include "paint.h"
using namespace std;
string solve_puzzle (string s, vector<int> c) {
int n = s.length(), k = c.size();
s = 'X' + s + 'X';
vector<vector<bool>> dp(n+2,vector<bool>(k+1)), dp2(n+2,vector<bool>(k+1));
vector<int> psa(n+1);
for (int i = 1; i <= n; i++) psa[i] = psa[i-1] + (s[i] == '_');
dp[0][0] = 1;
for (int i = 1; i <= n; i++) {
if (s[i] != 'X') dp[i][0] = dp[i-1][0];
if (s[i] != 'X') dp[i][1] = dp[i-1][1];
if (i >= c[0] && psa[i] == psa[i-c[0]]) dp[i][1] = dp[i][1] | dp[i-c[0]][0];
for (int j = 2; j <= k; j++) {
if (s[i] != 'X') dp[i][j] = dp[i-1][j];
if (i - c[j-1] >= 1 && psa[i] == psa[i-c[j-1]] && s[i-c[j-1]] != 'X')
dp[i][j] = dp[i][j] | dp[i-c[j-1]-1][j-1];
}
}
dp2[n+1][0] = 1;
for (int i = n; i >= 1; i--) {
if (s[i] != 'X') dp2[i][0] = dp2[i+1][0];
if (s[i] != 'X') dp2[i][1] = dp2[i+1][1];
if (i + c[k-1] - 1 <= n && psa[i + c[k-1] - 1] == psa[i-1]) dp2[i][1] = dp2[i][1] | dp2[i+c[k-1]][0];
for (int j = 2; j <= k; j++) {
if (s[i] != 'X') dp2[i][j] = dp2[i+1][j];
if (i + c[k-j] <= n && psa[i+c[k-j]-1] == psa[i-1] && s[i+c[k-j]] != 'X')
dp2[i][j] = dp2[i][j] | dp2[i+c[k-j]+1][j-1];
}
}
vector<int> diff(n+2);
for (int j = 1; j <= k; j++) {
for (int i = 1; i + c[j-1] - 1 <= n; i++) if (psa[i+c[j-1]-1]==psa[i-1]&& (j == 1 || s[i-1] != 'X') && (j == k || s[i + c[j-1]] != 'X') && dp[i-1-(j!=1)][j-1] && dp2[i+c[j-1]+(j!=k)][k-j]){
diff[i]++; diff[i+c[j-1]]--;
}
}
for (int i = 1; i <= n; i++) {
diff[i] += diff[i-1];
bool white = 0, black = diff[i];
for (int j = 0; j <= k; j++) {
white |= s[i] != 'X' && dp[i-1][j] && dp2[i+1][k-j];
}
assert(white || black);
s[i] = white && black ? '?' : (white ? '_' : 'X');
}
return s.substr(1,n);
}
