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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;

public class Main {

	public static void main(String[] args) throws IOException {
		// Mapに1,長さ 2, 長さ…というように入れる
		// valueソートする
		// 小さい長さから引いていき、解けるか確認
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String t1 = br.readLine();
		String[] temp1 = t1.split(" ");
		String[] temp2 = br.readLine().split(" ");
		int num = Integer.parseInt(temp1[0]);
		int len = Integer.parseInt(temp1[1]);
		int rope = 0;

		Map<Integer, Integer> map = new HashMap<Integer, Integer>();
		for(int i = 0; i < num; i++){
			rope += Integer.parseInt(temp2[i]);
			map.put(i, Integer.parseInt(temp2[i]));
		}
		// ソート
		List<Entry<Integer, Integer>> sortList = mapValueSort(map);
		ArrayList<Integer> showList = new ArrayList<Integer>();
		int knot = map.size() - 1;
		while(true){
			int i = 0;
			if(knot == 0){
				System.out.println("Possible");
				for(Integer j : showList){
					System.out.println(j);
				}
				break;
			}else if(knot != 0 && rope < len){
				System.out.println("Impossible");
				break;
			}else{
				rope -= sortList.get(i).getValue();
				showList.add(sortList.get(i).getKey());
				i++;
				knot--;
			}
		}
	}

	public static List<Entry<Integer, Integer>> mapValueSort(Map<Integer, Integer> map){
		//Map.Entryのリストを作成する
        List<Entry<Integer, Integer>> list_entries = new ArrayList<Entry<Integer, Integer>>(map.entrySet());

        //昇順
        Collections.sort(list_entries, new Comparator<Entry<Integer, Integer>>() {
            public int compare(Entry<Integer, Integer> obj1, Entry<Integer, Integer> obj2) {
                return obj1.getValue().compareTo(obj2.getValue());
            }
        });

        /*
        //降順
        Collections.sort(list_entries, new Comparator<Entry<Integer, Integer>>() {
            //compareを使用して値を比較する
            public int compare(Entry<Integer, Integer> obj1, Entry<Integer, Integer> obj2)
            {
                return obj2.getValue().compareTo(obj1.getValue());
            }
        });
        */
		return list_entries;
	}
}