#include "paint.h"
#include <bits/stdc++.h>
using namespace std;
#define ll int
#define F first
#define S second
#define sz(x) (ll)x.size()
#define pb push_back
typedef vector <ll> vi;
typedef pair <ll,ll> ii;
typedef vector <ii> vii;
#define dbg(x) cout<<#x<<": "<<x<<endl;
#define dbg2(x,y) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<endl;
#define dbg3(x,y,z) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<" "<<#z<<": "<<z<<endl;
void printVct(vi &v){
for (ll i= 0; i<sz(v); i++){
cout<<v[i]<<" ";
}
cout<<endl;
}
vi c;
ll fill_in(ll k, ll init_x, ll s, ll e, ll u = -1){
// dbg3(k, s, e);
ll p = s; //posisition of last black
ll x = init_x; //block index
if (u == -1){ //just fill in
while (x < k && p + c[x] + 1 < e){
p += c[x] + 1;
x++;
}
}
else{ //include black u
// dbg(u);
while (x < k-1 && p + 1 + c[x] < u-1){
p += c[x] + 1;
x++;
}
// dbg(p);
p = max(p + c[x] + 1, u);
// dbg(p);
if (p >= e){
if (x == init_x) return x;
p = u;
}
else{
x++;
}
while (x < k && p + c[x] + 1 < e){
p += c[x] + 1;
x++;
}
}
return x;
}
bool checkWhite(ll n, ll k, ll i, vi &whitePoints){
ll x = 0;
bool done_i = false;
ll prev = -1;
for (ll j =0; j<sz(whitePoints); j++){
if (!done_i && i < whitePoints[j]){
x = fill_in(k, x, prev-1, i);
prev = i;
done_i = true;
}
x = fill_in(k, x, prev-1, whitePoints[j]);
prev = whitePoints[j];
}
return (x >= k);
}
bool checkBlack(ll n, ll k, ll i, vi &whitePoints){
for (ll w = 0; w<k; w++){
ll x = 0;
bool done_i = false;
ll prev = -1;
bool ok = true;
for (ll j =0; j<sz(whitePoints); j++){
// dbg(j);
if (!done_i && i < whitePoints[j]){
ll prevX = x;
x = fill_in(k, x, prev-1, whitePoints[j], i);
if (x == prevX){
ok = false;
break;
}
done_i = true;
}
else{
if (!done_i){
x = fill_in(w, x, prev-1, whitePoints[j]);
}
else{
x = fill_in(k, x, prev-1, whitePoints[j]);
}
}
prev = whitePoints[j];
}
if (x >= k && ok) return true;
}
return false;
}
string solve_puzzle(string s, vi v) {
c = v;
ll n = sz(s);
ll k = sz(c);
vi whitePoints;
for (ll i =0; i<n; i++){
if (s[i] == '_') whitePoints.pb(i);
}
whitePoints.pb(n);
string ans;
ans.resize(n);
for (ll i =0; i<n; i++){
if (s[i] == '_'){
ans[i] = '_';
continue;
}
bool w = checkWhite(n,k,i,whitePoints);
bool b = checkBlack(n,k,i,whitePoints);
if (w && b) ans[i] = '?';
else if (w) ans[i] = '_';
else ans[i] = 'X';
// cout<<endl<<endl;
}
return ans;
}
/*
..._._....
1 3
.._._.....................
2 1 19
..........._._......................._...._........_._.___..........._..................
2 1 19
_........_
3 2 2 2
....._.
2 2 2
..........
3 1 3 2
*/
