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: Wrong Answer)

package main

import (
	"fmt"
	"strconv"
)

var coef = 1

func main() {
	var n, m int
	fmt.Scan(&n, &m)

	sn := strconv.Itoa(n)

	for i := 0; i < len(sn); i++ {
		coef *= 10
	}

	var arr []int
	for i := 0; i < m; i++ {
		var j, k int
		fmt.Scan(&j, &k)
		arr = append(arr, j*coef+k)
	}

	if search(arr, 1, n) {
		fmt.Println("POSSIBLE")
		return
	}

	fmt.Println("IMPOSSIBLE")
}

func search(arr []int, n int, target int) bool {
	for _, v := range arr {
		if t := v - n*coef; t < 10 && t > 0 {
			if t == target {
				return true
			}
			if n == 1 && search(arr, t, target) {
				return true
			}
		}
	}
	return false
}