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 <iomanip>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <numeric>
#include <random>
#include <vector>
#include <array>
#include <bitset>
#include <queue>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>

using namespace std;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n==0) ? 1 : 10*TEN(n-1); }
int bsr(int x) { return 31 - __builtin_clz(x); }

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(20);
    int n, l;
    cin >> n >> l;
    int a[n];
    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) {
            cout << "Possible" << endl;
            for (int j = 0; j < i; j++) {
                cout << j+1 << endl;
            }
            for (int j = n-1; j >= i+1; j--) {
                cout << j << endl;
            }
            return 0;
        }
    }
    cout << "Impossible" << endl;
    return 0;
}