#include <bits/stdc++.h>
using namespace std;
long long int pw(long long int a, long long int b, long long int mod) {
  if (!b) return 1;
  if (b & 1) return a * pw(a * a % mod, b / 2, mod) % mod;
  return pw(a * a % mod, b / 2, mod) % mod;
}
const long long int MAXN = 3e5 + 10;
const long long int INF = 8e18;
const long long int MOD = 1e9 + 7;
int n, m, k, comp[MAXN], timer, mark[MAXN];
vector<int> adj[MAXN];
set<int> remain;
void DFS(int u, int c) {
  comp[u] = c;
  vector<int> now;
  for (int v : remain) {
    auto x = lower_bound(adj[u].begin(), adj[u].end(), v);
    if (x != adj[u].end() && *x == v) continue;
    now.push_back(v);
  }
  for (int v : now) remain.erase(v);
  for (int v : now) DFS(v, c);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cin >> n >> m >> k;
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  for (int i = 1; i <= n; i++) {
    sort(adj[i].begin(), adj[i].end());
    if (i > 1) remain.insert(i);
  }
  while (!remain.empty()) {
    int u = *remain.begin();
    remain.erase(u);
    DFS(u, timer++);
  }
  if (timer > k || k > n - adj[1].size() - 1)
    return cout << "impossible" << '\n', 0;
  for (int i = 2; i <= n; i++) {
    auto x = lower_bound(adj[1].begin(), adj[1].end(), i);
    if (x != adj[1].end() && *x == i) continue;
    mark[comp[i]] = 1;
  }
  for (int i = 0; i < timer; i++) {
    if (!mark[i]) return cout << "impossible" << '\n', 0;
  }
  cout << "possible" << '\n';
  return 0;
}
