#include <bits/stdc++.h>
using namespace std;
set<pair<int, int> > fo;
vector<bool> vis;
set<int> a;
int c = 0;
bool ss(int u, int v) {
  if (u < v) swap(u, v);
  return fo.count({u, v});
}
void dfs(int u) {
  vector<int> w;
  for (auto i : a) {
    if (ss(u, i)) continue;
    w.push_back(i);
  }
  for (auto i : w) a.erase(i);
  for (auto i : w) {
    vis[i] = 1;
    dfs(i);
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  int x = n - 1;
  for (int i = (0), ThxMK = (m); i < ThxMK; ++i) {
    int a, b;
    cin >> a >> b;
    if (a < b) swap(a, b);
    fo.insert({a, b});
    if (a == 1 or b == 1) x--;
  }
  for (int i = (2), ThxMK = (n + 1); i < ThxMK; ++i) a.insert(i);
  vis = vector<bool>(n + 1, 0);
  vis[1] = 1;
  for (int i = (2), ThxMK = (n + 1); i < ThxMK; ++i)
    if (!ss(1, i) and !vis[i]) {
      dfs(i);
      c++;
    }
  for (int i = (1), ThxMK = (n + 1); i < ThxMK; ++i)
    if (!vis[i]) {
      cout << "impossible" << '\n';
      return 0;
    }
  if (c <= k and k <= x)
    cout << "possible" << '\n';
  else
    cout << "impossible" << '\n';
}
