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

$1\le X\le N$
$1\le K\le M\le 2\cdot {10}^{11}$
$1\le f_i\le 1000000$
$f_1+f_2+\cdots +f_N=M$

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%]

$1\le N\le 2000$

Subtask 5 [40%]

$1\le N\le 200000$

Input Specification

The first line will contain four 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