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>
using namespace std;
using ll = long long;
using db = double;
#define fi first
#define se second
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define siz(v) (ll)(v).size()
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define repn(i,n) for(ll i=0;i<=(ll)(n);i++)
typedef pair<int,int> P;
typedef pair<ll,ll> PL;
const ll mod = 1000000007;
const ll INF = 1000000099;
//cin.tie(0);
//ios::sync_with_stdio(false);



signed main(){
    ll n,m;cin>>n>>m;
    vector<int> v(n+1,0);
    rep(i,m){
        ll a,b;cin>>a>>b;
        if(a==1)v[b]++;
        if(b==n)v[a]++;
    }

    rep(i,n){
        if(v[i]>=2){
            cout<<"POSSIBLE"<<endl;
            return 0;
        }
    }
    cout<<"IMPOSSIBLE"<<endl;
}