E. Stack Sorting
constructive algorithms; data structures; greedy; implementation
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 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.
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.
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.