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 Kotlin (1.0.0) (judge verdict: Accepted)


fun main(args: Array<String>) {
    val (n, m) = readListInt()
    val ab = readMatrixInt(m)
    var boxA = mutableSetOf<Int>()
    var boxB = mutableSetOf<Int>()
    ab.forEach {
        if (it[0] == 1) boxA.add(it[1])
        if (it[1] == n) boxB.add(it[0])
    }

    if (boxA.find { boxB.contains(it) } != null) {
        println("POSSIBLE")
    } else {
        println("IMPOSSIBLE")
    }
}

private fun read() = readLine()!!

private fun readInt() = Integer.parseInt(read())

private fun readLong() = read().toLong()

private fun readDouble() = read().toDouble()

private fun readListString() = read().split(" ")

private fun readListInt() = readListString().map { Integer.parseInt(it) }

private fun readListLong() = readListString().map { it.toLong() }

private fun readListDouble() = readListString().map { it.toDouble() }

private fun readMatrixString(n: Int): List<List<String>> {
    val matrix = mutableListOf<List<String>>()
    for (i in 0 until n) {
        val list = readListString()
        matrix.add(list)
    }
    return matrix
}

private fun readMatrixInt(n: Int): List<List<Int>> {
    val matrix = mutableListOf<List<Int>>()
    for (i in 0 until n) {
        val list = readListInt()
        matrix.add(list)
    }
    return matrix
}

private fun readMatrixDouble(n: Int): List<List<Double>> {
    val matrix = mutableListOf<List<Double>>()
    for (i in 0 until n) {
        val list = readListDouble()
        matrix.add(list)
    }
    return matrix
}

private fun readMatrixLong(n: Int): List<List<Long>> {
    val matrix = mutableListOf<List<Long>>()
    for (i in 0 until n) {
        val list = readListLong()
        matrix.add(list)
    }
    return matrix
}