Let's suppose you have an array a, a stack s (initially empty) and an array b (also initially empty).

You may perform the following operations until both a and s are empty:

Take the first element of a, push it into s and remove it from a (if a is not empty); Take the top element from s, append it to the end of array b and remove it from s (if s is not empty).

You can perform these operations in arbitrary order.

If there exists a way to perform the operations such that array b is sorted in non-descending order in the end, then array a is called stack-sortable.

For example, [3, 1, 2] is stack-sortable, because b will be sorted if we perform the following operations:

Remove 3 from a and push it into s; Remove 1 from a and push it into s; Remove 1 from s and append it to the end of b; Remove 2 from a and push it into s; Remove 2 from s and append it to the end of b; Remove 3 from s and append it to the end of b.

After all these operations b = [1, 2, 3], so [3, 1, 2] is stack-sortable. [2, 3, 1] is not stack-sortable.

You are given k first elements of some permutation p of size n (recall that a permutation of size n is an array of size n where each integer from 1 to n occurs exactly once). You have to restore the remaining n - k elements of this permutation so it is stack-sortable. If there are multiple answers, choose the answer such that p is lexicographically maximal (an array q is lexicographically greater than an array p iff there exists some integer k such that for every i < k q_{i} = p_{i}, and q_{k} > p_{k}). You may not swap or change any of first k elements of the permutation.

Print the lexicographically maximal permutation p you can obtain.

If there exists no answer then output -1.

-----Input-----

The first line contains two integers n and k (2 ≤ n ≤ 200000, 1 ≤ k < n) — the size of a desired permutation, and the number of elements you are given, respectively.

The second line contains k integers p_1, p_2, ..., p_{k} (1 ≤ p_{i} ≤ n) — the first k elements of p. These integers are pairwise distinct.

-----Output-----

If it is possible to restore a stack-sortable permutation p of size n such that the first k elements of p are equal to elements given in the input, print lexicographically maximal such permutation.

Otherwise print -1.

-----Examples-----

Input 5 3 3 2 1

Output 3 2 1 5 4 Input 5 3 2 3 1

Output -1

Input 5 1 3

Output 3 2 1 5 4 Input 5 2 3 4

Output -1