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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
using namespace std;

const int MAX = 100000;
int main() {
	int N, a[MAX], L;
	cin >> N >> L;
	for (int i = 0;i < N;i ++) cin >> a[i];
	
	for (int i = 0;i < N - 1;i ++) {
		if (a[i] + a[i + 1] >= L) { // この区間を基準にできる
			cout << "Possible" << endl;
			for (int j = 1;j <= i;j ++) cout << j << endl;
			for (int j = N - 1;j > i + 1;j --) cout << j << endl;
			cout << i + 1 << endl;
			return 0;
		}
	}
	cout << "Impossible" << endl;
	return 0;
}
/*
31536000のコメント解説欄
ここテンプレで用意してるから、A問題とかだとこの先空欄の危険あり
また、コンテスト後に https://31536000.hatenablog.com/ で解説していると思うので、良かったら読んでねー

ある区間[a_i, a_i+1]の長さがL以上であるとする
この時、その区間を常に含むように区間を取り端から結び目をほどけば、答えが導出できる
逆に、そのような区間が存在しない時は最後の2区間になった時に結び目がほどけない
*/