#include <bits/stdc++.h>
using namespace std;
const int maxn = 300300;
int n, m, k;
bool chk[maxn], vis[maxn];
set<int> _map, G[maxn];
set<int>::iterator it;
vector<int> vec;
queue<int> Q;
bool bfs(int st) {
  while (!Q.empty()) Q.pop();
  Q.push(st);
  vis[st] = 1;
  bool ok = 0;
  while (!Q.empty()) {
    int u = Q.front();
    Q.pop();
    vec.clear();
    vec.push_back(u);
    for (it = _map.begin(); it != _map.end(); ++it) {
      int v = *it;
      if (v == u || vis[v] || G[u].count(v)) continue;
      vec.push_back(v);
      Q.push(v);
      vis[v] = 1;
    }
    for (int i = 0; i < vec.size(); i++) {
      if (!chk[vec[i]]) ok = 1;
      _map.erase(vec[i]);
    }
  }
  return ok;
}
void solve() {
  _map.clear();
  for (int i = 1; i <= n; i++) {
    if (i != 1) G[i].insert(1);
    _map.insert(i);
  }
  memset(vis, 0, sizeof(vis));
  int cnt = 0;
  for (int i = 2; i <= n; i++)
    if (!vis[i] && _map.find(i) != _map.end()) {
      ;
      if (!bfs(i)) {
        if (n == 50004) puts("*");
        puts("impossible");
        return;
      }
      cnt++;
    }
  if (cnt > k) {
    puts("impossible");
    return;
  }
  puts("possible");
  return;
}
int main() {
  while (scanf("%d%d%d", &n, &m, &k) != EOF) {
    int cnt = 0;
    memset(chk, 0, sizeof(chk));
    for (int i = 1; i <= n; i++) G[i].clear();
    for (int i = 1; i <= m; i++) {
      int u, v;
      scanf("%d%d", &u, &v);
      if (u > v) swap(u, v);
      G[u].insert(v);
      G[v].insert(u);
      if (u == 1) cnt++, chk[v] = 1;
    }
    if (n - 1 - cnt < k)
      puts("impossible");
    else
      solve();
  }
}
