#include <bits/stdc++.h>
using namespace std;
int n, m, k;
set<int> p[3111111];
int q[3111111], tou, wei;
set<int> node;
set<int>::iterator it;
int del[3111111], cnt;
vector<int> block[3111111];
void solve() {
  node.clear();
  for (int i = 2; i <= n; i++) node.insert(i);
  tou = wei = 0;
  if (p[1].size() > n - 1 - k) {
    printf("impossible\n");
    return;
  }
  int block_cnt = 0;
  while (node.size() > 0) {
    block_cnt++;
    tou = wei = 0;
    q[wei++] = *node.begin();
    node.erase(q[tou]);
    block[block_cnt].push_back(q[tou]);
    while (tou < wei) {
      int u = q[tou++];
      cnt = 0;
      for (it = node.begin(); it != node.end(); it++) {
        int v = *it;
        if (!p[u].count(v)) {
          del[cnt++] = v;
          q[wei++] = v;
          block[block_cnt].push_back(v);
        }
      }
      for (int i = 0; i < cnt; i++) node.erase(del[i]);
    }
  }
  int tot = 0;
  for (int i = 1; i <= block_cnt; i++) {
    bool flag = 0;
    for (int j = 0; j < block[i].size(); j++) {
      if (!p[1].count(block[i][j])) {
        tot++;
        flag = 1;
        break;
      }
    }
    if (!flag) {
      printf("impossible\n");
      return;
    }
  }
  printf("%s\n", tot <= k ? "possible" : "impossible");
}
int main() {
  while (scanf("%d%d%d", &n, &m, &k) == 3) {
    for (int i = 1; i <= n; i++) {
      p[i].clear();
      block[i].clear();
    }
    for (int i = 1; i <= m; i++) {
      int u, v;
      scanf("%d%d", &u, &v);
      p[u].insert(v);
      p[v].insert(u);
    }
    solve();
  }
  return 0;
}
