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 <sstream>
#include <stdio.h>
#include <map>
#include <vector>
#define rep(x,y) for(int x = 0; x < (y); x++)
#define REP(x,z,y) for(int x = (z); x < (y); x++)
#define all(x) x.begin(),x.end()
#define length(x) (sizeof(x) / sizeof(x[0]))
#define split_str(str,sp_word) istringstream stream(str); string res; while(getline(stream,res,sp_word))
#define rm_space(x) x.erase(remove(all(x),' '),x.end())

using namespace std;

int N,M;
map<int,vector<int>> ab; 

void dsp(int now, int cnt){
  if(cnt > 2) return;

  for(auto i:ab[now]){
    if(i == N){
      printf("POSSIBLE\n");
      exit(0);
    }
    dsp(i,cnt + 1);
  }
};

int main(){
  scanf("%d%d",&N,&M);
  rep(i,M){
    int tmp,tmp2;
    scanf("%d%d",&tmp,&tmp2);
    ab[tmp].push_back(tmp2);
  }

  dsp(1,1);
  printf("IMPOSSIBLE\n");
  return 0;
}