Problem:
Problem Statement

We have N pieces of ropes, numbered 1 through N. The length of piece i is a_i.

At first, for each i (1≤i≤N-1), piece i and piece i+1 are tied at the ends, forming one long rope with N-1 knots. Snuke will try to untie all of the knots by performing the following operation repeatedly:

Choose a (connected) rope with a total length of at least L, then untie one of its knots.

Is it possible to untie all of the N-1 knots by properly applying this operation? If the answer is positive, find one possible order to untie the knots.

Constraints

2≤N≤10^5

1≤L≤10^9

1≤a_i≤10^9

All input values are integers.

Input

The input is given from Standard Input in the following format:

N L
a_1 a_2 ... a_n

Output

If it is not possible to untie all of the N-1 knots, print Impossible.

If it is possible to untie all of the knots, print Possible, then print another N-1 lines that describe a possible order to untie the knots. The j-th of those N-1 lines should contain the index of the knot that is untied in the j-th operation. Here, the index of the knot connecting piece i and piece i+1 is i.

If there is more than one solution, output any.

Sample Input 1

3 50
30 20 10

Sample Output 1

Possible
2
1

If the knot 1 is untied first, the knot 2 will become impossible to untie.

Sample Input 2

2 21
10 10

Sample Output 2

Impossible

Sample Input 3

5 50
10 20 30 40 50

Sample Output 3

Possible
1
2
3
4

Another example of a possible solution is 3, 4, 1, 2.

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (N, L) = readInputLine().split(" ").map { it.toInt() }
    val a = readInputLine().split(" ").map { it.toInt() }.toIntArray()

    val ties = IntArray(N - 1) { a[it] + a[it + 1] }

    if (ties.all { it < L }) {
        println("Impossible")
        return
    } else {
        println("Possible")
    }

    // 最後にほどく結び目
    val lastTies = mutableSetOf<Int>()

    var l = 0
    var r = N - 2

    // まず左から最初に長さ和Lの結び目までほどく
    while (ties[l] < L) {
        println(l + 1)
        l++
    }
    lastTies.add(l)
    l++

    // 次に右から最初に長さ和Lの結び目までほどく
    while (ties[r] < L) {
        println(r + 1)
        r--
    }
    lastTies.add(r)
    r--

    // 左から長さ和がL未満の結び目を貪欲にほどく
    while (l <= r) {
        if (ties[l] < L) {
            println(l + 1)
        } else {
            lastTies.add(l)
        }
        l++
    }

    // 最後にほどく結び目をほどく
    for (t in lastTies) {
        println(t + 1)
    }
}

fun readInputLine(): String {
    return readLine()!!
}