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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <cstring>
#include <sstream>
#include <map>
#include <queue>
#include <set>
#include <vector>
#include <stack>
#include <cstdio>
using namespace std;
typedef long long int ll;
typedef pair<ll, ll> pos;
const ll MOD = 1000000007, N = 100000, dx[4] = { -1,1,0,0 }, dy[4] = { 0,0,-1,1 };

ll mn(ll a, ll b) {
	if (a == -1)return b;
	if (b == -1)return a;
	return min(a, b);
}
ll gcd(ll v1, ll v2) {
	if (v1 == 0)return v2; if (v2 == 0)return v1; if (v2 > v1)return gcd(v2%v1, v1); return gcd(v1%v2, v2);
}

struct ab {
	ll a, b;
	bool operator<(const ab& right) const {
		return right.b*a - right.a*b < 0;
	}
};

ll n, l[N],ld;

int main() {
	cin >> n >> ld;
	for (int i = 0; i < n; i++)cin >> l[i];
	for (int i = 0; i < n - 1; i++){
		if (l[i] + l[i + 1] >= ld) {
			cout << "Possible" << endl;
			for (int j = 1; j <= i; j++) {
				cout << j << endl;
			}
			for (int j = n - 1; j >= i + 2;j--)cout << j << endl;
			cout << i+1 << endl;
			return 0;
		}
	}
	cout << "mpossible" << endl;
	return 0;
}