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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
list($N, $L) = explode(" ", trim(fgets(STDIN)));
$a = array_merge([0], explode(" ", trim(fgets(STDIN))));;

$last = false;
for($i = 1; $i <= $N - 1; $i++){
    if($L <= $a[$i] + $a[$i + 1]){
        $last = $i;
        break;
    }
}
if(!$last){
    echo 'Impossible' . "\n";
}else{
    echo 'Possible' . "\n";
    for($i = $N - 1; $last < $i; $i--){
        echo $i . "\n";
    }
    for($i = 1; $i < $last; $i++){
        echo $i . "\n";
    }
    echo $last . "\n";
}