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 Python (3.4.3) (judge verdict: Wrong Answer)

#!/usr/bin/env python3


def solve(n, l, xs):
    pair_idx = None
    for i in range(n - 1):
        if xs[i] + xs[i + 1] >= l:
            pair_idx = i
            break
    if pair_idx is None:
        return (False, [])
    ans = [x + 1 for x in range(pair_idx)]
    ans.extend(x + 1 for x in range(pair_idx + 1, n - 1))
    ans.append(pair_idx + 1)
    return (True, ans)


def main():
    n, l = map(int, input().split())
    xs = list(map(int, input().split()))
    judge, ans = solve(n, l, xs)
    if not judge:
        print("Impossible")
        return
    print("Possible")
    for a in ans:
        print(a)


if __name__ == '__main__':
    main()