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 PHP (5.6.30) (judge verdict: Accepted)

<?php
/*
    Problem URL : http://agc002.contest.atcoder.jp/tasks/agc002_c

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

fscanf(STDIN, "%d %d", $N, $L);
$a = explode(" ", trim(fgets(STDIN)));
$p = null;
$mmax = 0;

for ($i = 0; $i < $N - 1; $i++) {
    $tmp = $a[$i] + $a[$i+1];
    $mmax = max($mmax, $tmp);
    if ($tmp >= $L) {
        $p = $i;
    }
}

if ($mmax >= $L) {
    echo "Possible\n";
} else {
    exit("Impossible\n");
}

$arr1 = $p > 0 ? range(1, $p) : array();
$arr2 = range($N-1, $p+1);
echo implode(PHP_EOL, array_merge($arr1, $arr2)) . PHP_EOL;