You have a sorted list of numbers in increasing order from to . This list has elements. Some numbers may appear multiple times, so you have recorded the number of occurrences of each number in this list, . However, you messed up when assigning the indices, so is actually the number of occurrences of , for some unknown permutation of . You recall that for some and . Find a permutation that satisfies this. If no such permutation exists, output `-1`

.

**You will be rewarded even if you can only determine the existence of such a .** Outputting any permutation of 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

##### Subtask 1 [10%]

##### Subtask 2 [20%]

##### Subtask 3 [20%]

##### Subtask 4 [10%]

##### Subtask 5 [40%]

#### Input Specification

The first line will contain three space-separated integers , , , and .

The next line will contain space-separated integers .

#### Output Specification

If there exists a permutation, output space-separated integers . 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 :

```
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 . The corresponding which gives this list is .

#### 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`

## Comments