#include <bits/stdc++.h>
#define INF 10000000000000000
#define MOD 1000000017
#define mid(l, u) ((l+u)/2)
#define rchild(i) (i*2 + 2)
#define lchild(i) (i*2 + 1)
using namespace std;
int n, k;
vector<int> cc;
string str;
int sum[200005];
int prevb[200005];
int dp[200005][105];
bool white[200005];
int black[200005];
//Condition is if (i-1) started between (ind[i]-c[i-1]+1)
int f(int i, int j){
//cout<<"f("<<i<<", "<<j<<") ";
if(j>=k && i>n){
return 1;
}
if(i>n){
//cout<<i<<" "<<n<<" i has exceeded n"<<endl;
return 0;
}
if(dp[i][j]!=-1){
//cout<<i<<" "<<j<<" dp[i][j] is already defined as "<<dp[i][j]<<endl;
return dp[i][j];
}
if(j>=k){
if(str[i]=='X') return dp[i][j] = 0;
int temp = f(i+1, j);
if(temp==1) white[i-1] = true;
return dp[i][j] = temp;
}
if(str[i-1]=='_'){
//cout<<"This index can only be white"<<endl;
int temp = f(i+1, j);
if(temp>=1) white[i-1] = true;
return dp[i][j] = temp;
}
if((i+cc[j]-1)>n){
//cout<<i<<" "<<cc[j]<<" out of bounds"<<endl;
return dp[i][j] = 0;
}
int ans = 0;
if(((sum[i+cc[j]-1] - sum[i-1])==0) && ((i+cc[j]<=n)?(str[i+cc[j]-1]!='X'):true)) {
int temp = f(i+cc[j]+1, j+1);
if(temp>=1){
black[i-1]++;
black[i+cc[j]-1]--;
white[i+cc[j]-1] = true;
//cout<<"it's possible to place a block at "<<i<<endl;
}
ans+=temp;
//cout<<"placing piece here "<<ans<<endl;
}
if(str[i-1]!='X'){
int temp = f(i+1, j);
if(temp>=1){
white[i-1] = true;
}
ans+=temp;
}
if(ans>=1) ans = 1;
//cout<<"dp["<<i<<"]["<<j<<"] = "<<dp[i][j]<<endl;
return dp[i][j] = ans;
}
string solve_puzzle(string s, vector<int> c){
str = s;
cc = c;
k = c.size();
n = s.length();
s[0] = 0;
for(int i = 0;i<n;i++){
if(s[i]=='_'){
sum[i+1]=1;
}
else sum[i+1] = 0;
sum[i+1]+=sum[i];
//cout<<(i+1)<<" "<<sum[i+1]<<endl;
}
for(int i = 0;i<=n;i++){
for(int j = 0;j<=k;j++){
dp[i][j] = -1;
}
}
int ind = 0;
for(int i = 1;i<=n;i++){
prevb[i] = ind;
if(s[i-1]=='X') ind = i;
}
for(int i = 0;i<=n;i++) white[i] = false;
for(int i = 0;i<=n;i++) black[i] = 0;
f(1, 0);
string ans = s;
for(int i = 0;i<n;i++) ans[i] = '?';
for(int i = 1;i<n;i++) black[i]+=black[i-1];
for(int i = 0;i<n;i++){
if(black[i]==0) ans[i] = '_';
if(white[i]==false) ans[i] = 'X';
//cout<<i<<" "<<black[i]<<" "<<white[i]<<endl;
}
for(int i = 1;i<=n;i++){
for(int j = 0;j<k;j++){
//cout<<"dp["<<i<<"]["<<j<<"] = "<<dp[i][j]<<endl;
}
}
return ans;
}
