E. Stack Sorting
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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:

  1. Remove 3 from a and push it into s;
  2. Remove 1 from a and push it into s;
  3. Remove 1 from s and append it to the end of b;
  4. Remove 2 from a and push it into s;
  5. Remove 2 from s and append it to the end of b;
  6. 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 qi = pi, and qk > pk). 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 p1, p2, ..., pk (1 ≤ pi ≤ 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