This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx,popcnt,sse4,abm")
#include <bits/stdc++.h>
#include "messy.h"
using namespace std;
#define ll long long
#define Waimai ios::sync_with_stdio(false), cin.tie(0)
#define FOR(x,a,b) for (int x = a, I = b; x <= I; x++)
#define pb emplace_back
#define F first
#define S second
vector<int> restore_permutation(int n, int w, int r) {
    vector<int> p(n, -1);
    auto ask = [&](auto ask, int l, int r)->void {
        if (l == r) return;
        string s(n, '0');
        FOR (i, 0, l - 1) s[i] = '1';
        FOR (i, r + 1, n - 1) s[i] = '1';
        int mid = (l + r) / 2;
        FOR (i, l, mid) {
            s[i] = '1';
            add_element(s);
            s[i] = '0';
        }
        ask(ask, l, mid);
        ask(ask, mid + 1, r);
    };
    ask(ask, 0, n - 1);
    compile_set();
    auto rec = [&](auto rec, int l, int r, vector<int> cand)->void {
        if (l == r) {
            p[l] = cand[0];
            return;
        }
        string s(n, '1');
        for (int x : cand) s[x] = '0';
        vector<int> nc[2];
        for (int x : cand) {
            s[x] = '1';
            nc[!check_element(s)].pb(x);
            s[x] = '0';
        }
        int mid = (l + r) / 2;
        rec(rec, l, mid, nc[0]);
        rec(rec, mid + 1, r, nc[1]);
    };
    vector<int> cand(n), tmp;
    iota(cand.begin(), cand.end(), 0);
    rec(rec, 0, n - 1, cand);
    tmp = p;
    FOR (i, 0, n - 1) p[tmp[i]] = i;
    return p;
}
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