#include "souvenirs.h"
#include <utility>
#include <vector>
#include <iostream>
std::pair<std::vector<int>, long long> specialTransaction(long long M, std::vector<int> &cnt, std::vector<long long> &price);
void half(long long P0, int target, std::vector<int> &cnt, std::vector<long long> &price, std::vector<std::pair<std::vector<int>, long long>> &equations);
void subtask3(int N, long long P0) {
// Subtask 3
std::vector<int> cnt(N, 0);
std::vector<int> price(N, 0);
long long current_price = P0 - 1;
while (price[N-1] == 0) {
std::pair<std::vector<int>, long long> res = transaction(current_price);
for (auto x: res.first) {
cnt[x]++;
}
if (res.first.size() == 1 && res.second == 0) {
int i = res.first[0];
price[i] = current_price;
current_price --;
} else {
int i = res.first[0];
price[i] = current_price - 1;
current_price -= 2;
}
}
for (int i=1; i<N; i++) {
for (int j = cnt[i]; j < i; j++) {
transaction(price[i]);
}
}
}
void subtask5(int N, long long P0) {
// Subtask 5
std::vector<int> cnt(N, 0);
std::vector<std::pair<std::vector<int>, long long>> equations;
std::vector<long long> price(N+1, 0); price[0] = P0; price[N] = 1;
half(P0, N-1, cnt, price, equations);
for (int i=N-2; i>1; i--) {
if (price[i]) continue;
std::pair<std::vector<int>, long long> res = specialTransaction(2*price[i+1], cnt, price);
if (res.first.size() == 1) {
price[i] = price[i+1]*2 - res.second;
continue;
}
int zeros = 0, ind = -1;
long long part = 0;
std::vector<int> asd;
for (int x: res.first) {
if (!price[x]) {
zeros++;
ind = x;
asd.push_back(x);
} else {
part += price[x];
}
}
if (zeros == 1) {
price[ind] = price[i+1]*2 - (res.second + part);
} else {
equations.push_back(std::pair(asd, res.second - part));
}
}
for (int i=0; i<N; i++) {
while (cnt[i] < i) {
transaction(price[i]);
cnt[i]++;
}
}
}
std::pair<std::vector<int>, long long> specialTransaction(long long M, std::vector<int> &cnt, std::vector<long long> &price) {
std::pair<std::vector<int>, long long> res = transaction(M);
for (auto x: res.first) {
cnt[x]++;
}
if (res.first.size() == 1) {
price[res.first[0]] = M - res.second;
}
return res;
}
bool simplify(std::vector<std::pair<std::vector<int>, long long>> &equations, std::vector<long long> &price) {
std::vector<std::pair<std::vector<int>, long long>> equations2;
for (auto pp: equations) {
if (pp.first.size() < 1) continue;
if (pp.first.size() == 1) {
price[pp.first[0]] = pp.second;
continue;
}
int zeros = 0, ind = -1;
long long part = 0;
std::vector<int> asd;
for (int x: pp.first) {
if (!price[x]) {
zeros++;
ind = x;
asd.push_back(x);
} else {
part += price[x];
}
}
if (zeros == 1) {
price[ind] = pp.second - part;
} else {
if (pp.second - part == 0) continue;
equations2.push_back(std::pair(asd, pp.second - part));
}
}
if (equations2.size() != equations.size()) {
equations = equations2;
return true;
} else {
for (int i=0; i<equations.size(); i++) {
if (equations[i].second != equations2[i].second) {
equations = equations2;
return true;
}
}
return false;
}
}
void half(long long current_price, int target, std::vector<int> &cnt, std::vector<long long> &price, std::vector<std::pair<std::vector<int>, long long>> &equations) {
while (price[target] == 0) {
std::pair<std::vector<int>, long long> res = specialTransaction(current_price, cnt, price);
std::vector<int> asd;
long long part = res.second;
for (int x: res.first) {
if (price[x]) {
part += price[x];
} else {
asd.push_back(x);
}
}
if (asd.size() > 0) {
equations.push_back(std::pair(asd, current_price - part));
}
if (!asd.size()) {
int temp = res.first[0];
for (int x: res.first) {
if (x >= target) break;
temp = x;
}
current_price = price[temp] - 1;
} else {
current_price = (current_price - part)/asd.size();
}
simplify(equations, price);
}
}
void resolve_all(std::vector<std::pair<std::vector<int>, long long>> &equations, std::vector<long long> &price, std::vector<int> &cnt) {
while(equations.size()) {
while(true) {
bool flag = false;
simplify(equations, price);
for (auto pp: equations) {
for (int x: pp.first) {
if (price[x]) {
flag = true;
}
}
}
if (!flag) {
break;
}
}
std::vector<int> num = equations[0].first;
long long sum = equations[0].second;
half(sum/num.size(), num[num.size()-1], cnt, price, equations);
simplify(equations, price);
}
}
void subtask6(int N, long long P0) {
// Subtask 6
std::vector<int> cnt(N, 0);
std::vector<std::pair<std::vector<int>, long long>> equations;
std::vector<long long> price(N+1, 0); price[0] = P0; price[N] = 1;
half(P0-1, N-1, cnt, price, equations);
resolve_all(equations, price, cnt);
for (int i=0; i<N; i++) {
while (cnt[i] < i) {
transaction(price[i]);
cnt[i]++;
}
}
}
void buy_souvenirs(int N, long long P0) {
if (N == 2) {
// Subtask 1
transaction(P0 - 1);
} else if (P0 == N) {
// Subtask 2
for (long long i = N-1, k = 1; i>0; i--, k++) {
for (int j = 0; j < k; j++) {
transaction(i);
}
}
} else if (N == 3) {
// Subtask 4
std::pair<std::vector<int>, long long> res = transaction(P0-1);
long long price = P0-1-res.second;
if (res.first.size() == 1) {
transaction(price-1);
transaction(price-1);
} else {
long long special = price / 2;
transaction(special);
}
} else {
subtask6(N, P0);
}
}
