#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "paint.h"
struct PREFIXSUM {
VI pref[3];
PREFIXSUM(string s) {
int n = s.size();
pref[0] = pref[1] = pref[2] = VI(n+1);
rep(i, n) {
if (s[i] == '_') pref[0][i+1]++;
else if (s[i] == 'X') pref[1][i+1]++;
else if (s[i] == '.') pref[2][i+1]++;
pref[0][i+1] += pref[0][i];
pref[1][i+1] += pref[1][i];
pref[2][i+1] += pref[2][i];
}
}
int count(int l, int r, string s) {
int ret = 0;
for (char ch : s) if (ch == '_') ret += pref[0][r+1] - pref[0][l];
else if (ch == 'X') ret += pref[1][r+1] - pref[1][l];
else if (ch == '.') ret += pref[2][r+1] - pref[2][l];
return ret;
};
};
VVI solve(string s, VI c) {
PREFIXSUM pref(s);
int n = s.size();
int k = c.size();
VVI dp(n+1, VI(k+1));
dp[0][0] = true;
replr(i, 1, n) {
if (s[i-1] == 'X') break;
dp[i][0] = true;
}
replr(i, 1, n) replr(j, 1, k) {
if (s[i-1] != 'X') dp[i][j] |= dp[i-1][j];
int sz = c[j-1];
if (i-sz < 0 || pref.count(i-sz, i-1, "_")) continue;
if (i-sz == 0) dp[i][j] |= dp[0][j-1];
else if (s[i-sz-1] != 'X') dp[i][j] |= dp[i-sz-1][j-1];
}
return dp;
}
string solve_puzzle(string s, VI c) {
s = "_" + s + "_";
int n = s.size();
int k = c.size();
VVI dpl = solve(s, c);
reverse(all(s));
reverse(all(c));
VVI dpr = solve(s, c);
reverse(all(s));
reverse(all(c));
PREFIXSUM pref(s);
VI lus(n);
VI rus(n);
if (true) {
int last;
replr(i, 0, n-1) {
if (s[i] == '_') last = i;
lus[i] = last;
}
reprl(i, n-1, 0) {
if (s[i] == '_') last = i;
rus[i] = last;
}
}
VVI payman(k, VI(n+1));
rep(j, k) replr(i, 1, n-c[j]-1) {
payman[j][i] = (
s[i-1] != 'X' &&
s[i+c[j]] != 'X' &&
dpl[i-1][j] &&
dpr[n-i-c[j]-1][k-j-1]);
payman[j][i] += payman[j][i-1];
}
string ans(n, '?');
replr(i, 1, n) {
if (s[i] != '.') ans[i] = s[i];
else {
bool a = false;
replr(j, 0, k-1) {
int L = max({1, i-c[j]+1, lus[i]+1});
int R = min({n-2, i+c[j]-1, rus[i]-1}) - c[j]+1;
if (payman[j][R] - payman[j][L-1]) a = true;
}
bool b = false;
replr(j, 0, k) {
if (dpl[i][j] && dpr[n-i-1][k-j]) {
b = true;
}
}
if (a && !b) ans[i] = 'X';
else if (!a && b) ans[i] = '_';
}
}
ans = ans.substr(1, n-2);
/*string real; cin >> real; if (real != ans) rep(i, 1000) cout << "ALERT ";*/
return ans;
}
