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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

int main(){
  int n, m;  scanf("%d %d", &n, &m);
  /*
  int **graph;
  graph = (int**)malloc(sizeof(int*)*(n+3));
  for(int i=0; i<n+3; i++){
    graph[i] = (int*)malloc(sizeof(int)*(n+3));
    for(int j=0; j<n+3; j++)
      graph[i][j] = 0;
  }
  */
  int from1[200003] = {0};
  int toN[200003] = {0};
  for(int i=0; i<m; i++){
    int f, t;
    scanf("%d %d", &f, &t);
    //    graph[f][++graph[f][0]] = t;
    if(f == 1){
      from1[++from1[0]] = t;
    }else if(t == n){
      toN[++toN[0]] = f;
    }
  }

  for(int i=from1[0]; i>=1; i--){
    for(int j=toN[0]; j>=1; j--){
      if(from1[i] == toN[j]){
	printf("POSSIBLE\n");
	return 0;
      }
    }
  }
  printf("IMPOSSIBLE\n");
  return 0;
}