#include <bits/stdc++.h>
using namespace std;
#define lf "\n"
#define ff endl
#define _ << ' ' <<
#define all(x) begin(x),end(x)
#define rall(x) rbegin(x),rend(x)
#define infot(str) do { fprintf(stderr, str); } while(0)
#define infos(str) do { fprintf(stderr, str"\n"); } while(0)
#define infor(str, ...) do { fprintf(stderr, str, __VA_ARGS__); } while(0)
#define infof(str, ...) do { fprintf(stderr, str"\n", __VA_ARGS__); } while(0)
#ifndef DEBUG
#undef infot
#undef infos
#undef infor
#undef infof
#define infot(str)
#define infos(str)
#define infor(str, ...)
#define infof(str, ...)
#endif
using ll = long long;
constexpr int LOG = 20;
constexpr int MOD = 1e9+7;
constexpr int MAXN = 1e5+7;
pair<vector<int>, long long> transaction(long long M);
void buy_souvenirs(int N, long long P0) {
vector<ll> minP(N); iota(rall(minP), 1);
vector<ll> maxP(N); iota(rall(maxP), P0 - (N - 1));
minP[0] = P0;
vector<int> cnt(N);
auto update_minP = [&](int v, ll x) -> void {
infof("update_minP(%d, %lld)", v, x);
for(; v > 0; v--) {
minP[v] = max(minP[v], x);
x = minP[v] + 1;
}
};
auto update_maxP = [&](int v, ll x) -> void {
infof("update_maxP(%d, %lld)", v, x);
for(; v < N; ++v) {
maxP[v] = min(maxP[v], x);
x = maxP[v] - 1;
}
};
auto buy = [&](int v) -> void {
infof("============= buy(%d) =============", v);
infot("minP:");
for(auto x: minP)
infor(" %2lld", x);
infos("");
infot("maxP:");
for(auto x: maxP)
infor(" %2lld", x);
infos("");
ll q = maxP[v];
auto [V, r] = transaction(q);
for(auto x: V) cnt[x]++;
if(V.size() == 1) {
ll p = q - r;
update_minP(v, p);
update_maxP(v, p);
return;
}
ll sum = 0;
int last = N - 1;
for(int i = V.size() - 1; i >= 0; i--) {
if(last != V[i]) break;
sum += minP[last--];
}
if(last > v) update_minP(last, sum + r + 1);
sum = 0;
for(int i = 1; i < V.size(); ++i)
sum += minP[V[i]];
update_maxP(v, q - (sum + r));
};
for(int i = 0; i < N; ++i) {
while(cnt[i] < i) buy(i);
}
}
