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: Accepted)

import bisect
import copy
import heapq
import sys
import itertools
import math
import queue
input = sys.stdin.readline
sys.setrecursionlimit(1000000)
mod = 10 ** 9 + 7

def read_values(): return map(int, input().split())
def read_index(): return map(lambda x: int(x) - 1, input().split())
def read_list(): return list(read_values())
def read_lists(N): return [read_list() for n in range(N)]
def init_dp1(init, N): return [init for _ in range(N)]
def init_dp2(init, N, M): return [[init for _ in range(M)] for _ in range(N)]


def f(S, T):
    N = len(S)
    F = [[0 for _ in range(N)] for __ in range(N)]
    
    for i in range(N):
        for j in range(N):
            SS = S[i]
            TT = T[j]
            if TT == (0, 0):
                F[i][j] = 1 if SS == (0, 1) else 0
            elif TT == (0, 1):
                if SS == (1, 0):
                    return None
                F[i][j] = 1
            elif TT == (1, 0):
                if SS == (0, 1):
                    return None
                F[i][j] = 0
            else:
                F[i][j] = 0 if SS == (1, 0) else 1

    return F


def main():
    N, L = read_values()
    A = read_list()

    r = 0
    for i in range(N - 1):
        if A[i] + A[i + 1] >= L:
            r = i
            break
    else:
        print("Impossible")
        return

    print("Possible")
    
    for i in range(r):
        print(i + 1)
    for i in range(N - 2, r - 1, -1):
        print(i + 1)


if __name__ == "__main__":
    main()