#include <bits/stdc++.h>
using namespace std;
#define in ({int x=0;int c=getchar(),n=0;for(;!isdigit(c);c=getchar()) n=(c=='-');for(;isdigit(c);c=getchar()) x=x*10+c-'0';n?-x:x;})
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int l,int r){return l+rng()%(r-l+1);}
#define fasty ios_base::sync_with_stdio(0),cin.tie(0);
#define forinc(a,b,c) for(int a=b,_c=c;a<=_c;++a)
#define fordec(a,b,c) for(int a=b,_c=c;a>=_c;--a)
#define forv(a,b) for(auto&a:b)
#define fi first
#define se second
#define pb push_back
#define ii pair<int,int>
#define mt make_tuple
#define all(a) a.begin(),a.end()
#define reset(f, x) memset(f, x, sizeof(f))
#define gg exit(0);
#include "messy.h"
vector<int> restore_permutation(int n,int w,int r){
string s;
forinc(i,1,n) s+="0";
forinc(i,1,n){
s[i-1]='1';
add_element(s);
}
vector<int> val(n);
iota(all(val),1);
compile_set();
vector<int> pos(n), dd(n);
s.clear();
forinc(i,1,n) s+="0";
forinc(i,1,n){
shuffle(all(val),rng);
forv(j,val) if(!dd[j-1]){
s[j-1]='1';
if(check_element(s)){
pos[j-1]=i-1;
dd[j-1]=1;
break;
}
s[j-1]='0';
}
}
return pos;
}
