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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict'

function main(input) {
  input = input.split('\n').map(v => v.split(' ').map(v => ~~v))
  const n = input[0][0]
  // const M = input[0][1]
  const ships = input.slice(1, input.length)

  let setA = new Set()
  let setB = new Set()
  for (let i = 0; i < ships.length; i++) {
    if (ships[i][0] == 1) {
      setA.add(ships[i][1])
    }
    if (ships[i][1] == n) {
      setB.add(ships[i][0])
    }
  }
  // console.log(shipsA, shipsB)

  for (let i = 1; i < n; i++) {
    if (setA.has(i) && setB.has(i)) {

      console.log('POSSIBLE')
      return
    }
  }
  let ans = 'IMPOSSIBLE'
  console.log(ans)
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'))