#include "islands.h"
#include <variant>
#include <vector>
#include <queue>
#include <iostream>
using namespace std;
const int maxn = 1e5 + 10;
int seen[maxn], in_deg[maxn], out_deg[maxn];
int n, m;
vector < int > links[maxn], rev_links[maxn];
vector < pair < int, int > > graph[maxn];
vector < int > path[3], cycle[3];
int dfs(int node, int id, int root)
{
if (seen[node] != 0)
return node;
///cout << node << " : " << id << " : " << root << endl;
seen[node] = 1;
for (pair < int, int > dest : graph[node])
{
if (seen[dest.first] >= 0)
{
path[id].push_back(dest.second);
int up = dfs(dest.first, id, root);
if (id == 0)
{
if (up >= 0)
{
path[id].pop_back();
cycle[id].push_back(dest.second);
seen[node] = 2;
}
else
seen[node] = 0;
if (node != root)
{
if (up == node)
return - 1;
else
return up;
}
}
if (up >= 0 && seen[up] == 1)
{
path[id].pop_back();
cycle[id].push_back(dest.second);
if (node != root)
{
if (up == node)
return -1;
else
return up;
}
}
if (node != root || id == 1)
return up;
id ++;
}
}
return -1;
}
int clear_useless()
{
queue < int > q;
for (int i = 0; i < n; i ++)
{
if (!out_deg[i])
q.push(i);
}
int start = 0;
while(!q.empty() || out_deg[start] <= 1)
{
if (!q.empty())
{
int node = q.front();
q.pop();
seen[node] = -1;
for (int dest : rev_links[node])
{
out_deg[dest] --;
if (out_deg[dest] == 0)
q.push(dest);
}
}
while(out_deg[start] <= 1)
{
seen[start] = -1;
out_deg[start] = 0;
for (int dest : rev_links[start])
{
out_deg[dest] --;
if (out_deg[dest] == 0)
q.push(dest);
}
pair < int, int > nxt = make_pair(-1, 0);
for (pair < int, int > cur : graph[start])
{
if (seen[cur.first] != -1)
{
nxt = cur;
break;
}
}
if (nxt.first == -1)
return -1;
start = nxt.first;
path[2].push_back(nxt.second);
}
}
return start;
}
void append_to_end(vector < int > &base, vector < int > &to_add, int type)
{
if (type == 0)
{
for (int i = 0; i < to_add.size(); i ++)
base.push_back(to_add[i]);
}
else
{
for (int i = (int)(to_add.size()) - 1; i >= 0; i --)
base.push_back(to_add[i]);
}
}
std::variant<bool, std::vector<int>> find_journey(int N, int M, std::vector<int> U, std::vector<int> V)
{
n = N;
m = M;
for (int i = 0; i < M; i ++)
{
links[U[i]].push_back(V[i]);
rev_links[V[i]].push_back(U[i]);
in_deg[V[i]] ++;
out_deg[U[i]] ++;
graph[U[i]].push_back({V[i], i});
}
int root = clear_useless();
if (root < 0)
return false;
dfs(root, 0, root);
/** for (int i = 0; i < cycle[1].size(); i ++)
cout << cycle[1][i] << " ";
cout << endl;
exit(0);*/
vector < int > ans;
append_to_end(ans, path[2], 0);
append_to_end(ans, path[0], 0);
append_to_end(ans, cycle[0], 1);
append_to_end(ans, path[0], 1);
append_to_end(ans, path[1], 0);
if (cycle[1].empty())
{
int ver = V[path[1].back()];
int idx = 0;
while(V[cycle[0][idx]] != ver)
idx ++;
///cout << "here " << U[cycle[0][idx]] << " " << V[]
for (int i = idx; i < cycle[0].size(); i ++)
ans.push_back(cycle[0][i]);
for (int i = 0; i < idx; i ++)
ans.push_back(cycle[0][i]);
}
else
append_to_end(ans, cycle[1], 1);
append_to_end(ans, path[1], 1);
if (!cycle[1].empty())
{
append_to_end(ans, path[0], 0);
append_to_end(ans, cycle[0], 0);
append_to_end(ans, path[0], 1);
append_to_end(ans, path[1], 0);
append_to_end(ans, cycle[1], 0);
append_to_end(ans, path[1], 1);
}
append_to_end(ans, path[2], 1);
return ans;
}
