#include <bits/stdc++.h>
using namespace std;
const int N = 5e5 + 10;
int n, m, k, u, v, sp, ep, remain, back[N], nxt[N];
vector<int> nei[N], help;
vector<vector<int>> comp;
bool find(int v, int u) {
  int l = -1, r = nei[v].size();
  while (r - l > 1) {
    int c = (r + l) / 2;
    if (nei[v][c] == u) return true;
    if (nei[v][c] < u)
      l = c;
    else
      r = c;
  }
  return false;
}
void deletE(int u) {
  remain--;
  if (u == sp)
    sp = nxt[sp];
  else if (u == ep) {
    ep = back[ep];
    nxt[ep] = -1;
  } else {
    nxt[back[u]] = nxt[u];
    back[nxt[u]] = back[u];
  }
}
void dfs(int v) {
  help.push_back(v);
  vector<int> vec;
  int u = sp;
  while (u != -1) {
    if (find(v, u) == false) vec.push_back(u);
    u = nxt[u];
  }
  for (int u : vec) deletE(u);
  for (int u : vec) dfs(u);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m >> k;
  while (m--) {
    cin >> u >> v;
    nei[--u].push_back(--v);
    nei[v].push_back(u);
  }
  for (int i = 0; i < n; i++) {
    sort(nei[i].begin(), nei[i].end());
    back[i] = i - 1;
    nxt[i] = i + 1;
  }
  sp = 1;
  ep = n - 1;
  back[sp] = nxt[ep] = -1;
  remain = n - 1;
  while (remain) {
    help.clear();
    int dex = sp;
    deletE(sp);
    dfs(dex);
    comp.push_back(help);
  }
  int cnt = 0;
  for (int i = 1; i < n; i++) cnt += (find(0, i) == false);
  bool ok = !(cnt < k || comp.size() > k);
  for (int i = 0; i < comp.size(); i++) {
    bool check = false;
    for (int u : comp[i])
      if (find(0, u) == false) check = true;
    if (!check) ok = false;
  }
  if (!ok)
    cout << "impossible";
  else
    cout << "possible";
  return 0;
}
