/*input
........
2
3 4
*/
//plonk code for further modifications later
#include "paint.h"
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef tree<long long, null_type, less_equal<long long>, rb_tree_tag, tree_order_statistics_node_update> indexed_set;
#pragma GCC optimize("unroll-loops,no-stack-protector")
//order_of_key #of elements less than x
// find_by_order kth element
typedef long long int ll;
#define ld double
#define pii pair<int,int>
#define f first
#define s second
#define pb push_back
#define REP(i,n) for(ll i=0;i<n;i++)
#define REP1(i,n) for(int i=1;i<=n;i++)
#define FILL(n,x) memset(n,x,sizeof(n))
#define ALL(_a) _a.begin(),_a.end()
#define sz(x) (int)x.size()
const ll maxn=2e5+5;
const ll maxlg=__lg(maxn)+2;
const ll INF64=4e18;
const int INF=0x3f3f3f3f;
const ll MOD=(1e9+7);
const ll MOD2=1000002173;
const ld PI=acos(-1);
const ld eps=1e-9;
#define lowb(x) x&(-x)
#define MNTO(x,y) x=min(x,(__typeof__(x))y)
#define MXTO(x,y) x=max(x,(__typeof__(x))y)
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define GET_POS(c,x) (lower_bound(c.begin(),c.end(),x)-c.begin())
ll mult(ll a,ll b){
return ((a%MOD)*(b%MOD))%MOD;
}
ll mypow(ll a,ll b,ll MOD){
if(b<=0) return 1;
ll res=1LL;
while(b){
if(b&1) res=(res*a)%MOD;
a=(a*a)%MOD;
b>>=1;
}
return res;
}
bool dp[maxn][105],dps[maxn][105];
int px[maxn],pw[maxn],sx[maxn],sw[maxn];
bool w[maxn],b[maxn];
string s;
string solve_puzzle(string S, vector<int> c) {
s=S;
int n=sz(s),k=sz(c);
int cnt=0,cnt2=0;
REP(i,n){
cnt+=(s[i]=='X');
cnt2+=(s[i]=='_');
dp[i][0]=(cnt==0);
px[i]=cnt;
pw[i]=cnt2;
}
REP1(i,n-1) REP1(j,k){
if(s[i]=='X'){
if(i>=c[j-1] and s[i-c[j-1]]!='X' and pw[i]==pw[i-c[j-1]]){
dp[i][j]=dp[i-c[j-1]][j-1];
}
else{
dp[i][j]=0;
}
}
else if(s[i]=='_') dp[i][j]=dp[i-1][j];
else{
if(i>=c[j-1] and s[i-c[j-1]]!='X' and pw[i]==pw[i-c[j-1]]){
dp[i][j]=dp[i-c[j-1]][j-1];
}
else{
dp[i][j]=0;
}
dp[i][j]|=dp[i-1][j];
}
}
for(int i=n-1;i>=0;i--) sx[i]=sx[i+1]+(s[i]=='X'),sw[i]=sw[i+1]+(s[i]=='_'),dps[i][0]=(sx[i]==0);
reverse(ALL(c));
for(int i=n-1;i>=0;i--) REP1(j,k){
if(s[i]=='X'){
if(i+c[j-1]<n and s[i+c[j-1]]!='X' and sw[i]==sw[i+c[j-1]]){
dps[i][j]=dps[i+c[j-1]][j-1];
}
else{
dps[i][j]=0;
}
}
else if(s[i]=='_') dps[i][j]=dps[i-1][j];
else{
if(i+c[j-1]<n and s[i+c[j-1]]!='X' and sw[i]==sw[i+c[j-1]]){
dps[i][j]=dps[i+c[j-1]][j-1];
}
else{
dps[i][j]=0;
}
dps[i][j]|=dps[i-1][j];
}
}
reverse(ALL(c));
REP(i,n){
REP(j,k) if(dp[i-1][j] and dps[i+1][k-j]){
w[i]=1;
break;
}
}
REP(i,n){
}
return s;
}
