#include <bits/stdc++.h>
using namespace std;
int read() {
  int v = 0, f = 1;
  char c = getchar();
  while (c < 48 || 57 < c) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (48 <= c && c <= 57) v = (v << 3) + v + v + c - 48, c = getchar();
  return v * f;
}
const int N = 3e5 + 10;
set<int> S;
set<int> E[N];
int n, m, k;
void dfs(int u) {
  S.erase(u);
  int v = 0;
  while (1) {
    set<int>::iterator i = S.upper_bound(v);
    if (i == S.end()) break;
    v = *i;
    if (E[u].count(v)) continue;
    dfs(v);
  }
}
int main() {
  n = read(), m = read(), k = read();
  for (int i = 1; i <= m; i++) {
    int u = read(), v = read();
    E[u].insert(v);
    E[v].insert(u);
  }
  for (int i = 1; i <= n; i++) S.insert(i);
  dfs(1);
  if (!S.empty()) return puts("impossible"), 0;
  for (int i = 2; i <= n; i++) S.insert(i);
  int t1 = 0, t2 = 0;
  for (int i = 2; i <= n; i++)
    if (S.count(i)) dfs(i), t1++;
  t2 = n - 1 - E[1].size();
  if (t1 <= k && k <= t2)
    puts("possible");
  else
    puts("impossible");
}
