You have a sorted list ~A~ of numbers in increasing order from ~1~ to ~N~. This list has ~M~ elements. Some numbers may appear multiple times, so you have recorded the number of occurrences of each number in this list, ~f_1, f_2, \dots, f_N~. However, you messed up when assigning the indices, so ~f_i~ is actually the number of occurrences of ~P_i~, for some unknown permutation ~P~ of ~1, 2, \dots, N~. You recall that ~A_K=X~ for some ~K~ and ~X~. Find a permutation ~P~ that satisfies this. If no such permutation ~P~ exists, output -1.

You will be rewarded even if you can only determine the existence of such a ~P~. Outputting any permutation of ~1, 2, \dots, N~ if there exists a permutation and -1 otherwise for every test case of a subtask will earn you half of the subtask's points, assuming you do not already receive the full points (if one of the permutations outputted is wrong, but there does exist a permutation).

Constraints

~1 \le X \le N~
~1 \le K \le M \le 2 \cdot 10^{11}~
~1 \le f_i \le 1\,000\,000~
~f_1+f_2+\dots+f_N = M~

Subtask 1 [10%]

~1 \le N \le 8~

Subtask 2 [20%]

~1 \le N \le 20~

Subtask 3 [20%]

~1 \le N \le 400~

Subtask 4 [10%]

~1 \le N \le 2\,000~

Subtask 5 [40%]

~1 \le N \le 200\,000~

Input Specification

The first line will contain three space-separated integers ~N~, ~M~, ~K~, and ~X~.
The next line will contain ~N~ space-separated integers ~f_1, f_2, \dots, f_N~.

Output Specification

If there exists a permutation, output ~N~ space-separated integers ~P_1, P_2, \dots, P_N~. There may be many valid permutations. Any one of them will be accepted.
If there does not exist a permutation, output -1.

Sample Input 1

3 10 5 1
4 5 1

Sample Output 1

2 1 3

Explanation for Sample 1

There are six possible lists ~A~:

1 1 1 1 2 2 2 2 2 3
1 1 1 1 2 3 3 3 3 3
1 1 1 1 1 2 2 2 2 3
1 1 1 1 1 2 3 3 3 3
1 2 2 2 2 3 3 3 3 3
1 2 2 2 2 2 3 3 3 3

The third list satisfies ~A_K=X~. The corresponding ~P~ which gives this list is ~2, 1, 3~.

Sample Input 2

6 9 4 4
2 2 2 1 1 1

Sample Output 2

4 5 6 1 2 3

Sample Input 3

6 9 3 4
2 2 2 1 1 1

Sample Output 3

-1