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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

type edge struct {
	from int
	to   int
}

func main() {
	var N, M int
	fmt.Scan(&N, &M)
	m := make(map[edge]int, 2*N)
	var x, y int
	for i := 0; i < M; i++ {
		fmt.Scan(&x, &y)
		if x == 1 || y == N {
			e := edge{from: x, to: y}
			m[e]++
		}
	}

	found := false
	for i := 1; i <= N; i++ {
		if i == 1 {
			if m[edge{from: 1, to: N}] != 0 {
				found = true
				break
			}
		} else {
			if m[edge{from: 1, to: i}] != 0 && m[edge{from: i, to: N}] != 0 {
				found = true
				break
			}
		}
	}

	if found {
		fmt.Println("POSSIBLE")
	} else {
		fmt.Println("IMPOSSIBLE")
	}
}