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: Accepted)

#include <iostream>
#include <vector>

using namespace std;

vector<int> g[200000];
bool from1[200000];
bool fromn[200000];
int main(){
  int n,m;
  cin >> n >> m;

  for(int i=0;i<m;++i){
    int a,b;
    cin >> a >> b;
    g[a-1].push_back(b-1);
    g[b-1].push_back(a-1);
  }
  
  for(int i=0;i<g[0].size();++i){
    from1[g[0][i]] = true;
  }

  for(int i=0;i<g[n-1].size();++i){
    fromn[g[n-1][i]] = true;
  }
  
  for(int i=0;i<200000;++i){
    if(from1[i]&&fromn[i]){
      cout << "POSSIBLE" << endl;
      return 0;
    }
  }
  cout << "IMPOSSIBLE" << endl;
  return 0;
}