#include "paint.h"
#include <bits/stdc++.h>
using namespace std;
string solve_puzzle(string s, vector<int> c) {
int n = (int) s.length(), k = (int) c.size();
c.insert(c.begin(), 0);
s = '$' + s + '$';
vector< vector<int> > pre(n + 1, vector<int>(2, 0));
for (int i = 1; i <= n; i++) {
if (s[i] == '_') {
pre[i][0] = 1;
} else if (s[i] == 'X') {
pre[i][1] = 1;
}
pre[i][0] += pre[i - 1][0];
pre[i][1] += pre[i - 1][1];
}
vector< vector<int> > dp_left(k + 1, vector<int>(n + 1, 0)), dp_right(k + 2, vector<int>(n + 2, 0));
for (int j = 0; j <= n; j++) {
dp_left[0][j] = (pre[j][1] == 0);
}
for (int i = 1; i <= k; i++) {
for (int j = 1; j <= n; j++) {
int b1 = dp_left[i][j - 1];
int b2 = (j - c[i] >= 0 && pre[j][0] - pre[j - c[i]][0] == 0 && s[j - c[i]] != 'X');
if (i == 1) {
if (j - c[i] >= 1) {
b2 = b2 && dp_left[i - 1][j - c[i] - 1];
}
} else {
b2 = b2 && (j - c[i] >= 1 && dp_left[i - 1][j - c[i] - 1]);
}
if (s[j] == 'X') {
dp_left[i][j] = b2;
} else if (s[j] == '_') {
dp_left[i][j] = b1;
} else {
dp_left[i][j] = b1 || b2;
}
}
}
for (int j = n; j >= 1; j--) {
dp_right[k + 1][j] = (pre[n][1] - pre[j - 1][1] == 0);
}
dp_right[k + 1][0] = (pre[n][1] == 0);
dp_right[k + 1][n + 1] = 1;
for (int i = k; i >= 1; i--) {
for (int j = n; j >= 1; j--) {
int b1 = dp_right[i][j + 1];
int b2 = (j + c[i] <= n + 1 && pre[j + c[i] - 1][0] - pre[j - 1][0] == 0 && s[j + c[i]] != 'X');
if (i == k) {
if (j + c[i] <= n) {
b2 = b2 && dp_right[i + 1][j + c[i] + 1];
}
} else {
b2 = b2 && (j + c[i] <= n && dp_right[i + 1][j + c[i] + 1]);
}
if (s[j] == 'X') {
dp_right[i][j] = b2;
} else if (s[j] == '_') {
dp_right[i][j] = b1;
} else {
dp_right[i][j] = b1 || b2;
}
}
}
vector<int> white(n + 1), black(n + 1);
for (int j = 1; j <= n; j++) {
if (s[j] == 'X') {
white[j] = 0;
continue;
}
if (s[j] == '_') {
white[j] = 1;
continue;
}
for (int i = 0; i <= k; i++) {
if (dp_left[i][j - 1] && dp_right[i + 1][j + 1]) {
white[j] = 1;
break;
}
}
}
for (int i = 1; i <= k; i++) {
vector<int> tmp(n + 1, 0);
for (int j = 1; j + c[i] - 1 <= n; j++) {
if (s[j - 1] == 'X' || s[j + c[i]] == 'X') {
continue;
}
if (pre[j + c[i] - 1][0] - pre[j - 1][0] > 0) {
continue;
}
int b1, b2;
if (j == 1) {
b1 = (i == 1);
} else {
b1 = dp_left[i - 1][j - 2];
}
if (j + c[i] - 1 == n) {
b2 = (i == k);
} else {
b2 = dp_right[i + 1][j + c[i] + 1];
}
if (b1 && b2) {
for (int t = j + c[i] - 1; t >= j && !tmp[t]; t--) {
tmp[t] = 1;
}
}
}
for (int i = 1; i <= n; i++) {
black[i] = black[i] || tmp[i];
}
}
for (int i = 1; i <= n; i++) {
if (s[i] == '.') {
if (white[i] && black[i]) {
s[i] = '?';
} else if (white[i] && !black[i]) {
s[i] = '_';
} else if (!white[i] && black[i]) {
s[i] = 'X';
}
}
}
return s.substr(1, n);
}
