Problem:
Score : 300 points

Problem Statement

In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.
For convenience, we will call them Island 1, Island 2, ..., Island N.

There are M kinds of regular boat services between these islands.
Each service connects two islands. The i-th service connects Island a_i and Island b_i.

Cat Snuke is on Island 1 now, and wants to go to Island N.
However, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.

Help him.

Constraints

3 ≤ N ≤ 200 000

1 ≤ M ≤ 200 000

1 ≤ a_i < b_i ≤ N

(a_i, b_i) \neq (1, N)

If i \neq j, (a_i, b_i) \neq (a_j, b_j).

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

POSSIBLE

Sample Input 2

4 3
1 2
2 3
3 4

Sample Output 2

IMPOSSIBLE

You have to use three boat services to get to Island 4.

Sample Input 3

100000 1
1 99999

Sample Output 3

IMPOSSIBLE

Sample Input 4

5 5
1 3
4 5
2 3
2 4
1 4

Sample Output 4

POSSIBLE

You can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5.

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>
#include <vector>
#include <set>
using namespace std;
int main(){
  int n,m;
  cin >> n >> m;
  vector<pair<int,int>> ab(n);
  for(int i=0;i<m;i++) cin >> ab[i].first >> ab[i].second;

  vector<int> med;
  set<int> st;
  st.insert(0);
  for(int i=0;i<m;i++){
    if(ab[i].first == 1){
      med.emplace_back(ab[i].second);
    }
    if(ab[i].second == n){
      st.insert(ab[i].first);
    }
  }

  bool flag = false;
  for(int i=0;i<med.size();i++){
    auto itr = st.find(med[i]);
    if(itr != st.end()){
      flag = true;
      break;
    }
  }

  if(flag) cout << "POSSIBLE\n";
  else cout << "IMPOSSIBLE\n";
}