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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var n, l int
	fmt.Scan(&n, &l)
	as := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&as[i])
	}

	x := -1
	for i := 0; i < n-1; i++ {
		if l <= as[i]+as[i+1] {
			x = i
			break
		}
	}
	if x == -1 {
		fmt.Println("Impossible")
		return
	}

	ans := make([]int, 0)
	left, right := 0, n-2
	for left != right {
		if left < x {
			ans = append(ans, left)
			left++
		} else if x < right {
			ans = append(ans, right)
			right--
		}
	}
	ans = append(ans, x)

	fmt.Println("Possible")
	for i := 0; i < len(ans); i++ {
		fmt.Println(ans[i] + 1)
	}
}