/*************************************
* author: marvinthang *
* created: 22.11.2023 21:23:33 *
*************************************/
#include "koala.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i-- > 0; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
// end of template
int B[105], R[105];
int cache[2][205];
int num[2][205];
char taken[105][205];
int minValue(int N, int W) {
REP(i, N) B[i] = !i;
playRound(B, R);
FOR(i, 1, N) if (!R[i]) return i;
return 0;
}
int maxValue(int N, int W) {
vector <int> cur(N);
iota(ALL(cur), 0);
while (cur.size() > 1) {
memset(B, 0, N * sizeof(int));
int t = N / cur.size();
for (int x: cur) B[x] = t;
playRound(B, R);
cur.clear();
REP(i, N) if (R[i] > t) cur.push_back(i);
}
return cur[0];
}
int greaterValue(int N, int W) {
memset(B, 0, N * sizeof(int));
for (int v: {2, 5, 10}) {
B[0] = B[1] = v;
playRound(B, R);
int a = R[0] > v, b = R[1] > v;
if (a != b) return b;
if (v == 2 && !a) return !minValue(N, W);
}
return 0;
}
void allValues(int N, int W, int *P) {
if (W == 2*N) {
memset(B, 0, N * sizeof(int));
auto cmp = [&] (int x, int y) {
B[x] = B[y] = 100;
playRound(B, R);
B[x] = B[y] = 0;
return R[x] < R[y];
};
function <void(vector <int> &)> merge_sort = [&] (vector <int> &v) {
int n = v.size();
if (n <= 1) return;
int m = n >> 1;
vector <int> left(v.begin(), v.begin() + m);
vector <int> right(v.begin() + m, v.end());
merge_sort(left); merge_sort(right);
merge(ALL(left), ALL(right), v.begin(), cmp);
};
vector <int> order(N);
iota(ALL(order), 0);
merge_sort(order);
REP(i, N) P[order[i]] = i + 1;
} else {
auto cmp = [&] (int x, int y) -> bool {
memset(B, 0, N * sizeof(int));
for (int v: {10, 5, 2}) {
B[x] = B[y] = v;
playRound(B, R);
int a = R[x] > v, b = R[y] > v;
if (a != b) return b;
if (v == 2 && !a) return minValue(N, W) == x;
}
return false;
};
auto simulatePlayRound = [&](int *B, int *R) {
int S = 0;
int i,j;
for (i=0;i<N;++i) {
S += B[i];
}
for (i=0;i<205;++i) {
cache[1][i] = 0;
num[1][i] = 0;
}
for (i=0;i<N;++i) {
int v = B[i]+1;
int ii = i&1;
int o = ii^1;
for (j=0;j<=W;++j) {
cache[ii][j] = cache[o][j];
num[ii][j] = num[o][j];
taken[i][j] = 0;
}
for (j=W;j>=v;--j) {
int h = cache[o][j-v] + i + 1;
int hn = num[o][j-v] + 1;
if (h > cache[ii][j] || (h == cache[ii][j] && hn > num[ii][j])) {
cache[ii][j] = h;
num[ii][j] = hn;
taken[i][j] = 1;
} else {
taken[i][j] = 0;
}
}
}
int cur = W;
for (i=N-1;i>=0;--i) {
R[i] = taken[i][cur] ? (B[i] + 1) : 0;
cur -= R[i];
}
};
function <void(vector <int> &, int, int)> solve = [&] (vector <int> &v, int l, int r) {
if (v.size() <= 1) return;
int tl = 0, tr = W / (r - l);
memset(B, 0, N * sizeof(int));
FOR(i, l, r) B[i] = tr;
simulatePlayRound(B, R);
int cnt_left = 0, cnt_right = 0;
FOR(i, l, r) ++(R[i] <= B[i] ? cnt_left : cnt_right);
if (!cnt_right) {
while (tl <= tr) {
int m = tl + tr >> 1;
FOR(i, l, r) B[i] = m;
simulatePlayRound(B, R);
cnt_right = 0;
FOR(i, l, r) cnt_right += R[i] > B[i];
if (cnt_right == r - l) tl = m + 1;
else if (!cnt_right) tr = m - 1;
else {
tr = m;
break;
}
}
}
memset(B, 0, N * sizeof(int));
for (int x: v) B[x] = tr;
playRound(B, R);
vector <int> left, right;
for (int x: v) (R[x] <= B[x] ? left : right).push_back(x);
solve(left, l, l + (int) left.size());
solve(right, l + (int) left.size(), r);
v = left;
v.insert(v.end(), ALL(right));
};
vector <int> order(N);
iota(ALL(order), 0);
solve(order, 0, N);
REP(i, N) P[order[i]] = i + 1;
}
}
