#include <bits/stdc++.h>
// mrrrow meeow :3
// go play vivid/stasis now! https://vividstasis.gay
#define fo(i, a, b) for (auto i = (a); i < (b); i++)
#define of(i, a, b) for (auto i = (b); i-- > (a);)
#define f first
#define s second
#define pb push_back
#define pob pop_back
#define lb lower_bound
#define ub upper_bound
#define be(a) a.begin(), a.end()
using namespace std;
int ____init = [] {
ios::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
return 0;
}();
int n;
vector<int> c;
int empties[200001];
bool check_empty(int l, int r) {
return empties[min(r, n)] - empties[l];
}
int filled[200001];
bool check_filled(int l, int r) {
return filled[min(r, n)] - filled[l];
}
int bit_empties[200001];
int get_empty(int i) {
int res = 0;
for (i++; i > 0; i -= i & -i) res += bit_empties[i];
return res;
}
void add_empty(int i, int v) {
for (i++; i <= 200000; i += i & -i) bit_empties[i] += v;
}
int bit_filled[200001];
int get_filled(int i) {
int res = 0;
for (i++; i > 0; i -= i & -i) res += bit_filled[i];
return res;
}
void add_filled(int i, int v) {
for (i++; i <= 200000; i += i & -i) bit_filled[i] += v;
}
int checked[101];
int check(int i, int j) {
if (i >= c.size()) return 1;
checked[i] = j;
if (check_empty(j, j + c[i])) return 0;
int valids = 0;
of(k, j + c[i] + 1, checked[i + 1]) {
if (!check_filled(j + c[i], k)) {
int did = check(i + 1, k);
add_empty(j + c[i], did);
add_empty(k, -did);
valids += did;
}
}
add_filled(j, valids);
add_filled(j + c[i], -valids);
return valids;
}
string solve_puzzle(string s, vector<int> _c) {
n = s.size();
c = _c;
fo(i, 0, c.size()) checked[i] = n - c[i] + 1;
checked[c.size()] = n + 2;
fo(i, 0, n) {
empties[i + 1] = empties[i] + (s[i] == '_');
filled[i + 1] = filled[i] + (s[i] == 'X');
}
of(i, 0, checked[0]) if (!check_filled(0, i)) {
int did = check(0, i);
add_empty(0, did);
add_empty(i, -did);
}
string res(n, '?');
fo(i, 0, n) {
if (get_empty(i) == 0) res[i] = 'X';
else if (get_filled(i) == 0) res[i] = '_';
}
return res;
}
