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++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
const int MOD=1000000007;

int main() {
  int n,m;
  cin >> n >> m;
  vector<vector<int>> data(m, vector<int>(2));
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < 2; j++) {
      cin >> data.at(i).at(j);
    }
  }
  sort(data.begin(), data.end());
  for (int i = 0; i < m; i++) {
      if(data.at(i).at(0)==1){
        for (int j = i+1; j < m; j++){
          if(data[i][1]==data[j][0] && data[j][1]==n){
            cout << "POSSIBLE" << endl;
            return 0;
          }
        }
      }
      if(data.at(i).at(0)==2)
      break;
    }
    cout << "IMPOSSIBLE" << endl;
}