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 <bits/stdc++.h>
#define rep(i, s, n) for (int i = (s); i < (int)(n); i++)
#define per(i, n, s) for (int i = (n-1); i >= (int)(s); i--)
#define all(x) (x).begin(),(x).end()
#define debug(x) cout<<#x<<": "<<x<<endl
using namespace std;
using ll = long long;
const ll MOD = 1e9+7;
const ll LINF = LLONG_MAX;
const int INF = INT_MAX;

int main(){
    int n,m; cin>>n>>m;
    vector<set<int>> path(n);
    rep(i,0,m){
        int x,y; cin>>x>>y;
        x--; y--;
        path[x].insert(y);
        path[y].insert(x);
    }
    bool ok=false;
    for(auto &i:path[0]){
        if(path[i].count(n-1)) ok=true;
    }
    if(ok) cout<<"POSSIBLE"<<endl;
    else cout<<"IMPOSSIBLE"<<endl;
}