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 ways[200000];
int max;

int solve(int *a, int *b, int m, int n) {
  for(int k = 0; k < max; k++) {
    for(int i = 0; i < m; i++) {
      if(ways[k] == a[i] && b[i] == n) return 1;
    }
  }
  return 0;
}

int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  int *a = calloc(sizeof(int), m),
      *b = calloc(sizeof(int), m);
  int c = 0;
  for(int i = 0; i < m; i++) {
    scanf("%d %d", &a[c], &b[c]);
    if(a[c] == 1) {
      ways[max++] = b[c];
    } else c++;
  }
  puts(solve(a, b, c, n) ? "POSSIBLE" : "IMPOSSIBLE");
}