#include "paint.h"
#include <cstdlib>
#include <functional>
#include <iostream>
#include <cassert>
#define debug(x) #x << " = " << x << '\n'
const int NMAX = 2e5 + 2;
const int KMAX = 100 + 2;
bool pref[NMAX + 1][KMAX + 1][2];
bool suff[NMAX + 1][KMAX + 1][2];
int sumX[NMAX + 1];
int sum_[NMAX + 1];
bool makeX(int l, int r) {
return sum_[r] - sum_[l - 1] == 0;
}
bool make_(int l, int r) {
return sumX[r] - sumX[l - 1] == 0;
}
std::string solve_puzzle(std::string s, std::vector<int> c) {
int n = (int) s.size();
int k = (int) c.size();
s = '$' + s;
c.insert(c.begin(), 0);
std::string answer(n, '.');
for (int i = 1; i <= n; i++) {
sumX[i] = sumX[i - 1] + (s[i] == 'X'? +1 : 0);
sum_[i] = sum_[i - 1] + (s[i] == '_'? +1 : 0);
}
pref[0][0][0] = pref[0][0][1] = true;
for (int i = 1; i <= n; i++) {
for (int j = 0; j <= k + 1; j++) {
pref[i][j][0] = pref[i][j][1] = false;
}
if (s[i] == 'X') {
for (int j = 0; j <= k + 1; j++) {
if (j != 0 && i - c[j] >= 0) {
pref[i][j][1] |= (pref[i - c[j]][j - 1][0] & makeX(i - c[j] + 1, i));
}
}
} else if (s[i] == '_') {
for (int j = 0; j <= k + 1; j++) {
pref[i][j][0] |= pref[i - 1][j][0];
pref[i][j][0] |= pref[i - 1][j][1];
}
} else {
for (int j = 0; j <= k + 1; j++) {
pref[i][j][0] |= pref[i - 1][j][0];
pref[i][j][0] |= pref[i - 1][j][1];
if (j != 0 && i - c[j] >= 0) {
pref[i][j][1] |= (pref[i - c[j]][j - 1][0] & makeX(i - c[j] + 1, i));
}
}
}
}
suff[n + 1][k + 1][0] = suff[n + 1][k + 1][1] = true;
for (int i = n; i > 0; i--) {
for (int j = 0; j <= k + 1; j++) {
suff[i][j][0] = suff[i][j][1] = false;
}
if (s[i] == 'X') {
for (int j = 0; j <= k + 1; j++) {
if (j != 0 && i + c[j] <= n + 1) {
suff[i][j][1] |= (suff[i + c[j]][j + 1][0] & makeX(i, i + c[j] - 1));
}
}
} else if (s[i] == '_') {
for (int j = 0; j <= k + 1; j++) {
suff[i][j][0] |= suff[i + 1][j][0];
suff[i][j][0] |= suff[i + 1][j][1];
}
} else {
for (int j = 0; j <= k + 1; j++) {
if (j != 0 && i + c[j] <= n + 1) {
suff[i][j][1] |= (suff[i + c[j]][j + 1][0] & makeX(i, i + c[j] - 1));
}
}
for (int j = 0; j <= k + 1; j++) {
suff[i][j][0] |= suff[i + 1][j][0];
suff[i][j][0] |= suff[i + 1][j][1];
}
}
}
std::function<bool()> works = [&] () -> bool {
return pref[n][k][0] | pref[n][k][1];
};
assert(works());
for (int i = 1; i <= n; i++) {
if (s[i] != '.') {
answer[i - 1] = s[i];
continue;
}
bool worksX = false, works_ = false;
/// calculez works_
for (int j = 0; j <= k; j++) {
if ((pref[i - 1][j][0] || pref[i - 1][j][1]) && (suff[i + 1][j + 1][0] || suff[i + 1][j + 1][1])) {
works_ = true;
}
}
/// calculez worksX
for (int j = 1; j <= k && !worksX; j++) { /// in al catelea block ma aflu
for (int l = std::max(1, i - c[j] + 1); l <= i && !worksX; l++) { /// unde incepe blocku
if (pref[l - 1][j - 1][0] && suff[l + c[j]][j + 1][0] && makeX(l, l + c[j] - 1)) {
worksX = true;
}
}
}
if (worksX && works_) {
answer[i - 1] = '?';
} else if (worksX) {
answer[i - 1] = 'X';
} else {
answer[i - 1] = '_';
}
}
return answer;
}
/**
..........
2 3 4
........
2 3 4
..._._....
1 3
.X........
1 3
**/
