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>
#include <map> // pair
using namespace std;

typedef long long ll;
#define vec vector<int>
#define vecll vector<ll>
#define vpair vector<pair<int, int>>
#define vpairll vector<pair<ll, ll>>
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define rep(i,n)   for(int i=(int)0; i<(int)n; i++)
#define llrep(i,n)   for(ll i=(ll)0; i<(ll)n; i++)
#define REP(i,m,n) for(int i=(int)m; i<(int)n; i++)
#define all(var)     (var).begin(), (var).end()
#define prt(var)     cout << var << endl
#define prt_dbl(i,var) cout<<fixed<<setprecision(i)<<var<<endl;
template <typename Val,typename Number>
//use ll or int for gcd
Val gcd(Val a, Val b) {
    if (b==0) return a;
    else return gcd(b, a%b);
}
//count vector and return pair (count,vector item)
template <typename Val,typename Number>
void count_vector(vector<Val>* A,vector<pair<Number,Val>>*R){
  sort(A->begin(),A->end());
  int count = 1;
  rep(i,A->size()){
    if(i<A->size()-1){
      if(A->at(i)==A->at(i+1))count++;
      else{
        R->push_back(make_pair(count,A->at(i)));
        count = 1;
      }
    }else{
      R->push_back(make_pair(count,A->at(i)));
      count = 1;
    }
  }
}

//---------------------------------------------------------------

int main(){
  int N,M;
  cin>>N>>M;
  vector<vector<int>>A(N);
  string ans ="IMPOSSIBLE";
  rep(i,M){
    int a,b;
    cin>>a>>b;
    A.at(a-1).push_back(b);
  }

  if(A.at(0).size()>0){
    rep(i,A.at(0).size()){
      int to = A.at(0).at(i);
      if(A.at(to-1).size()>0){
        rep(j,A.at(to-1).size()){
          if(A.at(to-1).at(j)==N){
            ans = "POSSIBLE";
            break;
          }
        }
      }
    }
  }

  cout<<ans<<endl;




}