#include <iostream>
#include <iterator>
#include <memory>
#include <vector>
#include <deque>
#include <set>
#include <map>
#include <algorithm>
using namespace std;
void answer(int X);
void count_routes(int N, int M, int P, int R[][2], int Q, int G[]) {
// Build adjacency lists, but only keep up to 2 edges per node
vector<vector<int>> node_edges(N + 1);
for (int idx = 0; idx < M; ++idx) {
int i = R[idx][0];
int j = R[idx][1];
if (node_edges[i].size() < 2) {
node_edges[i].push_back(j);
}
if (node_edges[j].size() < 2) {
node_edges[j].push_back(i);
}
}
// Walk function: choose the neighbor that's not the one we came from
auto do_walk = [&](int walk, int prev_walk) {
if (node_edges[walk].empty()) {
// No neighbors, same
return walk;
}
int next_walk = node_edges[walk][0];
if (node_edges[walk].size() == 2 && next_walk == prev_walk) {
next_walk = node_edges[walk][1];
}
return next_walk;
};
map<pair<int, int>, int > state_to_cycle_start_pos;
map<pair<int, int>, int > state_to_path_pos;
map<pair<int, int>, std::shared_ptr< deque<pair<int, int>>> > state_to_path_with_cycle;
// Can we, starting from `node`, after g steps end up at node P?
auto can_from_node = [&](int node, int g) {
auto path = make_shared<deque<pair<int,int>>>();
set<pair<int,int>> visited;
int prev_walk = node;
int walk = do_walk(prev_walk, -1);
int next_walk = do_walk(walk, prev_walk); // uses default prev_walk = -1
while (g > 0) {
g--;
pair<int,int> state = make_pair(walk, next_walk);
if (state_to_path_pos.find(state) != state_to_path_pos.end()) { // cached
// std::cout << "hit cache!" << std::endl;
auto path_pos = state_to_path_pos[state];
auto cycle_start_pos = state_to_cycle_start_pos[state];
auto path_with_cycle = state_to_path_with_cycle[state];
auto c_size = state_to_path_with_cycle[state]->size() - cycle_start_pos;
// std::cout << "path pos " << path_pos << std::endl;
// std::cout << "curr node " << (*path_with_cycle)[path_pos].first << std::endl;
// std::cout << "cycle start pos " << cycle_start_pos << std::endl;
// std::cout << "cyle start node " << (*path_with_cycle)[cycle_start_pos].first << std::endl;
// std::cout << "g " << g << std::endl;
// std::cout << "got path: " << std::endl;
for (auto state_it = path_with_cycle->begin(); state_it != path_with_cycle->end(); ++state_it) {
// std::cout << (*state_it).first << " " << (*state_it).second << std::endl;
}
int g_rem;
if (path_pos >= cycle_start_pos) { // already in cycle
// std::cout << "already in cycle!" << std::endl;
g_rem = g + (path_pos - cycle_start_pos);
} else if (path_pos + g >= cycle_start_pos) { // can reach cycle
// std::cout << "can reach cycle" << std::endl;
g_rem = g - (cycle_start_pos - path_pos);
} else { // cannot reach cycle, pos + g < is in path
// std::cout << "cannot reach cycle" << std::endl;
return (*path_with_cycle)[path_pos + g].first == P; // no need for modulo
}
// std::cout << "c_size " << c_size << std::endl;
int idx = (cycle_start_pos) + (g_rem % c_size);
int res = (*path_with_cycle)[idx].first;
// std::cout << "using idx " << idx << std::endl;
// std::cout << "getting res " << res << std::endl;
return res == P;
}
if (visited.find(state) == visited.end()) {
visited.insert(state);
path->push_back(state);
int temp = walk;
walk = do_walk(walk, prev_walk);
if (temp == walk) {
return walk == P; // we are stuck at walk
}
prev_walk = temp;
next_walk = do_walk(walk, prev_walk);
} else {
// std::cout << "hit cycle!" << std::endl;
// std::cout << "g remaining " << g << std::endl;
// std::cout << "path: " << std::endl;
for (int i = 0; i < path->size(); i++) {
// std::cout << (*path)[i].first << " " << (*path)[i].second << std::endl;
}
// std::cout << "state: " << state.first << " " << state.second << std::endl;
auto cycle_start_it = std::find(path->begin(), path->end(), state);
auto cycle_start_pos = std::distance(path->begin(), cycle_start_it);
for (auto state_it = path->begin(); state_it != path->end(); ++state_it) {
// cache
auto path_pos = std::distance(path->begin(), state_it);
state_to_path_pos.insert({*state_it, path_pos});
state_to_cycle_start_pos.insert({*state_it, cycle_start_pos});
state_to_path_with_cycle.insert({*state_it, path});
}
int c = std::distance(cycle_start_it, path->end());
// std::cout << "cycle length " << c << std::endl;
return (*path)[(cycle_start_pos) + (g % c)].first == P;
}
}
// std::cout << "found path:" << '\n';
for (int i = 0; i < path->size(); i ++) {
// std::cout << (*path)[i].first << '\n';
}
// std::cout << "--------" << '\n';
// After g steps, are we at P?
return path->back().first == P;
};
for (int i = 0; i < Q; i++) {
int g_val = G[i];
int count = 0;
// std::cout << "i " << i << std::endl;
for (int node = 0; node < N; ++node) {
// std::cout << "can from node: " << node << " " << g_val << std::endl;
bool can = can_from_node(node, g_val);
// std::cout << "can from node " << node << " " << g_val << ": " << can << std::endl;
if (can) {
count++;
}
// std::cout << "--------------------" << std::endl;
}
answer(count);
// std::cout << "----------------------------------------" << std::endl;
}
}
