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>
#include<algorithm>
#include<iomanip>
#include<stack>
#include<queue>
#include<string>
#include<set>
#include<map>
using namespace std;
#define rep(i,n) for(int i=0;(i)<(n);(i)++)
#define FOR(i,m,n) for(int i=(m);(i)<(n);(i)++)
typedef long long ll;

int main(){
    int n,m;
    cin >> n >> m;
    vector<vector<int> > G(n);
    rep(i,m){
        int a,b;
        cin >> a >> b;
        a--;b--;
        G[a].push_back(b);
        G[b].push_back(a);
    }
    for(auto x:G[0]){
        for(auto y:G[x]){
            if(y==n-1){
                cout << "POSSIBLE" <<endl;
                return 0;
            }
        }
    }
    cout << "IMPOSSIBLE" << endl;
    return 0; 
}