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 (1.14.1) (judge verdict: Accepted)

// 隣り合うのをL以上になるようにくっつけていきたいね 一箇所でもみつければあとは隣接してるのをくっつけていきたいね
// -> てんでダメでした
// よくよくみたらおかしいところ 端から切り離す感じにするようにした
// -> なぜかWA
// 3つ並んでる総和がL未満なら見込み0ってことか
// -> そういうことではない

package main

import "fmt"

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

	idx := -1
	for i := 1; i < N; i++ {
		if A[i-1]+A[i] >= L {
			idx = i
			break
		}
	}

	if idx == -1 {
		fmt.Println("Impossible")
		return
	}
	P := []int{}
	for i := N - 1; i > idx; i-- {
		P = append(P, i)
	}
	for i := 1; i < idx; i++ {
		P = append(P, i)
	}
	P = append(P, idx)
	fmt.Println("Possible")
	for _, p := range P {
		fmt.Println(p)
	}
}

// 10 4
// 2 1 1 4 2 3 1 2 1 2

// 5 3
// 1 1 3 1 1

// 5 5
// 1 1 3 2 1