// -------------------- Includes -------------------- //
#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <stdio.h>
#include <cstdlib>
#include <stdlib.h>
#include <array>
#include <string>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <math.h>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <bitset>
#include <list>
#include <iterator>
#include <numeric>
#include <complex>
#include <tuple>
#include <utility>
#include <cassert>
#include <assert.h>
#include <climits>
#include <limits.h>
#include <ctime>
#include <time.h>
#include <random>
#include <chrono>
#include <fstream>
#include "paint.h"
using namespace std;
// -------------------- Typedefs -------------------- //
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ld;
// -------------------- Defines -------------------- //
#define pr pair
#define mpr make_pair
#define ff first
#define ss second
#define mset multiset
#define mmap multimap
#define uset unordered_set
#define umap unordered_map
#define umset unordered_multiset
#define ummap unordered_multimap
#define pqueue priority_queue
#define sz(x) (int((x).size()))
#define len(x) (int((x).length()))
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define clr(x) (x).clear()
#define pf push_front
#define pb push_back
#define popf pop_front
#define popb pop_back
#define ft front
#define bk back
#define lb lower_bound
#define ub upper_bound
#define bs binary_search
// -------------------- Constants -------------------- //
const int MAX = int(1e9 + 5);
const ll MAXL = ll(1e18 + 5);
const ll MOD = ll(1e9 + 7);
const ll MOD2 = ll(998244353);
// -------------------- Functions -------------------- //
void fastio()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
return;
}
void precision(int x)
{
cout.setf(ios::fixed | ios::showpoint);
cout.precision(x);
return;
}
ll gcd(ll a, ll b)
{
while (b) {
a %= b;
swap(a, b);
}
return a;
}
ll lcm(ll a, ll b)
{
return a / gcd(a, b) * b;
}
bool is_prime(ll a)
{
if (a == 1) {
return false;
}
for (ll i = 2; i * i <= a; i++) {
if (a % i == 0) {
return false;
}
}
return true;
}
bool is_square(ll a)
{
ll b = ll(sqrt(a));
return (b * b == a);
}
bool is_cube(ll a)
{
ll b = ll(cbrt(a));
return (b * b * b == a);
}
int digit_sum(ll a)
{
int sum = 0;
while (a) {
sum += int(a % 10);
a /= 10;
}
return sum;
}
ll binpow(ll a, int b)
{
ll ans = 1;
while (b) {
if ((b & 1) == 1) {
ans *= a;
}
b >>= 1;
a *= a;
}
return ans;
}
ll binpow_by_mod(ll a, ll b, ll mod)
{
ll ans = 1;
while (b) {
if ((b & 1) == 1) {
ans *= a;
ans %= mod;
}
b >>= 1;
a *= a;
a %= mod;
}
return ans;
}
ll factorial(int a)
{
ll ans = 1;
for (int i = 2; i <= a; i++) {
ans *= ll(i);
}
return ans;
}
ll factorial_by_mod(int a, ll mod)
{
ll ans = 1;
for (int i = 2; i <= a; i++) {
ans *= ll(i);
ans %= mod;
}
return ans;
}
// -------------------- Solution -------------------- //
const int N = 200005, K = 105;
int p[N];
int n, k;
bool dp[N][K][2];
bool a1[N], a2[N];
string solve_puzzle(string s, vector<int> c)
{
int i, j;
reverse(all(s));
s.pb(' ');
reverse(all(s));
n = len(s) - 1;
reverse(all(c));
c.pb(0);
reverse(all(c));
k = sz(c) - 1;
for (int h = 1; h <= n; h++) {
if (s[h] != '.') continue;
for (i = 1; i <= n; i++) p[i] = p[i - 1] + int(s[i] == '_');
s[h] = 'X';
for (i = 0; i <= n; i++) for (j = 0; j <= k; j++) dp[i][j][0] = dp[i][j][1] = false;
dp[0][0][0] = true;
for (i = 0; i < n; i++) {
for (j = 0; j <= k; j++) {
if (dp[i][j][0]) {
if (s[i + 1] == '_' || s[i + 1] == '.') {
dp[i + 1][j][0] = true;
}
if (s[i + 1] == 'X' || s[i + 1] == '.') {
if (j < k && i + c[j + 1] <= n && p[i + c[j + 1]] - p[i] == 0) {
dp[i + c[j + 1]][j + 1][1] = true;
}
}
}
if (dp[i][j][1]) {
if (s[i + 1] == '_' || s[i + 1] == '.') {
dp[i + 1][j][0] = true;
}
}
}
}
/*for (i = 0; i <= n; i++) {
for (j = 0; j <= k; j++) {
cout << i << ' ' << j << ' ' << dp[i][j][0] << ' ' << dp[i][j][1] << "\n";`
}
}*/
if (dp[n][k][0] || dp[n][k][1]) a1[h] = true;
//------------------------------------------
s[h] = '_';
for (i = h; i <= n; i++) p[i]++;
for (i = 0; i <= n; i++) for (j = 0; j <= k; j++) dp[i][j][0] = dp[i][j][1] = false;
dp[0][0][0] = true;
for (i = 0; i < n; i++) {
for (j = 0; j <= k; j++) {
if (dp[i][j][0]) {
if (s[i + 1] == '_' || s[i + 1] == '.') {
dp[i + 1][j][0] = true;
}
if (s[i + 1] == 'X' || s[i + 1] == '.') {
if (j < k && i + c[j + 1] <= n && p[i + c[j + 1]] - p[i] == 0) {
dp[i + c[j + 1]][j + 1][1] = true;
}
}
}
if (dp[i][j][1]) {
if (s[i + 1] == '_' || s[i + 1] == '.') {
dp[i + 1][j][0] = true;
}
}
}
}
if (dp[n][k][0] || dp[n][k][1]) a2[h] = true;
s[h] = '.';
}
string t = "";
for (i = 1; i <= n; i++) {
if (s[i] == '.') {
if (!a1[i]) t += '_';
else if (!a2[i]) t += 'X';
else t += '?';
}
else {
t += s[i];
}
}
return t;
}
/*
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*/
