#include "messy.h"
#include <iostream>
#include <vector>
#include <string>
#include <cassert>
using namespace std;
#define rep(i, n) for (int i=0; i<(n); i++)
#define INF 1145141919
vector<int> restore_permutation(int n, int w, int r) {
int x = n;
int logn = 0;
while (x>=2) logn++, x/=2;
assert(logn < n-logn);
string ones(n, '1');
rep(i, logn) {
ones[i] = '0';
assert(w-- > 0);
add_element(ones);
}
for (int i=logn; i<n; i++) {
string zeros(n, '0');
zeros[i] = '1';
//add_element(zeros);
rep(k, logn) if ((i>>k)&1) {
zeros[k] = '1';
assert(w-- > 0);
add_element(zeros);
}
}
vector<int> ret(n, -1), rev(n, -1);
compile_set();
string pat(n, '1');
rep(i, logn) {
int pos = -1;
rep(p, n) if (pat[p] == '1') {
pat[p] = '0';
assert(r-- > 0);
if (check_element(pat)) {
pos = p;
break;
}
pat[p] = '1';
}
assert(pos != -1 && rev[pos] == -1);
ret[i] = pos;
rev[pos] = i;
pat[pos] = '0';
}
rep(i, n) if (rev[i] == -1) {
string s(n, '0');
s[i] = '1';
//assert(check_element(s));
int pos = 0;
rep(j, logn) {
s[ret[j]] = '1';
assert(r-- > 0);
if (check_element(s)) {
pos |= 1<<j;
}
else s[ret[j]] = '0';
}
assert(ret[pos] == -1);
ret[pos] = i;
rev[i] = pos;
}
return rev;
}
