Restore the Original Sequence

Petya had a sequence of n integers, but he accidentally shuffled it. Fortunately, he remembers that the sum of the original sequence satisfied \(\sum_{i=1}^{n} a_i = s\) and that it contained exactly m unique integers. Given the shuffled sequence, your task is to restore any valid ordering of the sequence that meets both conditions, or report that it is impossible.

For example, if n = 5, m = 3, the shuffled sequence is [1, 2, 2, 3, 2], and s = 10, one valid restored sequence is [1, 2, 2, 3, 2] (note that any permutation of the input which satisfies the conditions is accepted). If no such permutation exists, output -1.

Note: The sequence's sum and its multiset remain unchanged under permutation. Therefore, the necessary and sufficient conditions for a valid sequence are:

\(\sum_{i=1}^{n} a_i = s \quad \text{and} \quad |\{a_1,a_2,\dots,a_n\}| = m\).

inputFormat

The first line contains three space-separated integers n, m, and s, where n is the length of the sequence, m is the number of distinct integers in the original sequence, and s is the sum of the sequence.

The second line contains n space-separated integers representing the shuffled sequence.

outputFormat

If a valid permutation exists, print the sequence as n space-separated integers in one line. Otherwise, print -1.

## sample

5 3 10
1 2 2 3 2

1 2 2 3 2

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