#include "paint.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ll mask){return __builtin_popcountll(mask);}
int ctz(ll mask){return __builtin_ctzll(mask);}
int logOf(ll mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
// mt19937_64 rng(69);
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T& container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
const int N = 2e5 + 69, K = 101;
bitset<N> dp[K], f[K];
string solve_puzzle(string s, vector<int> c){
s = "_" + s;
int n = s.size();
int k = c.size();
c.insert(c.begin(), 0);
s = "0" + s;
vector<int> pref(n+1);
for(int i= 1; i<=n; ++i) pref[i] = pref[i-1] + (s[i] == '.' || s[i] == 'X');
dp[0][0] = f[0][0] = 1;
for(int i= 1; i<=n; ++i) if (s[i] != 'X') dp[0][i] = dp[0][i-1] || dp[0][i];
for(int layer = 1; layer<=k; ++layer){
for(int i = c[layer] + 1; i<=n; ++i){
if (pref[i] - pref[i - c[layer]] == c[layer] && s[i - c[layer]] != 'X' && dp[layer - 1][i - c[layer] - 1]){
dp[layer][i] = f[layer][i] = 1;
}
}
for(int i= 1; i<=n; ++i) if (s[i] != 'X') dp[layer][i] = dp[layer][i-1] || dp[layer][i];
}
vector<int> sum[2];
for(auto &i: sum) i.resize(n+2);
vector<int> nxt(n+1);
for(int i = 1; i<=n; ++i){
nxt[i] = nxt[i-1];
if (s[i] == 'X') nxt[i] = i;
}
vector<int> mis; mis.push_back(n);
for(int layer = k; layer >= 1; --layer){
vector<int> rig(n+1, n + 2);
for(int i = n; i>=0; --i){
if (i < n) rig[i] = rig[i+1];
if (f[layer][i]) rig[i] = i;
}
vector<int> bruh(n+2);
for(int i: mis){
int j = nxt[i];
int k = rig[j];
if (k > i) continue;
sum[0][k+1]++; sum[0][i+1]--;
bruh[k]++; bruh[i+1]--;
}
for(int i= 1; i<=n+1; ++i) bruh[i] += bruh[i-1];
mis.clear();
for(int i= 1; i<=n; ++i) if (bruh[i] && f[layer][i]){
mis.push_back(i - c[layer] - 1);
sum[0][i - c[layer]]++; sum[0][i - c[layer] + 1]--;
sum[1][i - c[layer] + 1]++;
sum[1][i+1]--;
}
}
sum[0][1]++;
sum[0][mis.back()+1]--;
for(int j = 0; j<=1; ++j)
for(int i = 1; i<=n+1; ++i){
sum[j][i] += sum[j][i-1];
}
string ans = "";
for(int i = 2; i<=n; ++i){
if (sum[0][i] && sum[1][i]) ans.push_back('?');
else if (sum[0][i]) ans.push_back('_');
else ans.push_back('X');
}
return ans;
}
// int main(void){
// ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// string s; cin >> s;
// int k; cin >> k;
// vector<int> c(k);
// for(int i = 0; i<k; ++i) cin >> c[i];
// cout << solve_puzzle(s, c) << "\n";
// return 0;
// }
