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>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <limits.h>
#include <queue>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
#define REP(i, n) for(int i=0; i<n; i++)

ll A[100100];
int main(){
    ll N,L;
    cin >> N >> L;
    REP(i,N){
        ll a;
        cin >> a;
        A[i] = a;
    }

    //queue<ll> q;
    ll last = A[0];
    int pivot = -1;
    for(int i = 1; i < N; i++){
        ll a = A[i];
        if(last + a >= L){
            pivot = i-1;
            break;
        }
        last = a;
    }

    if(pivot < 0){
        cout << "Impossible" << endl;
        return 0;
    }

    cout << "Possible" << endl;
    for(int i = 0; i < pivot; i++){
        cout << i+1 << endl;
    }
    for(int i = N-2; i >= pivot; i--){
        cout << i+1 << endl;
    }
    return 0;
}