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"
	"bufio"
	"os"
	"strings"
	"strconv"
)

func main() {

	var N, L int
	fmt.Scan(&N, &L)
	a := make([]int, N)
	S := readLine()
	l := strings.Split(S, " ")
	for i := 0; i < N; i++ {
		a[i], _ = strconv.Atoi(l[i])
	}

	mi := 0

	possible := false
	for l := 0; l < N - 1; l++ {
		if a[l] + a[l + 1] >= L {
			possible = true
			mi = l
		}
	}

	if !possible {
		fmt.Println("Impossible")
		return
	}
	fmt.Println("Possible")
	for l := 1; l <= mi; l++ {
		fmt.Println(l)
	}
	for l := N - 1; l > mi; l-- {
		fmt.Println(l)
	}

}

var rdr = bufio.NewReaderSize(os.Stdin, 1000000)

func readLine() string {
	buf := make([]byte, 0, 1000000)
	for {
		l, p, e := rdr.ReadLine()
		if e != nil {
			panic(e)
		}
		buf = append(buf, l...)
		if !p {
			break
		}
	}
	return string(buf)
}