Educational Codeforces Round 35 (Rated for Div. 2)

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 calledstack-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 kelements 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

【題意】

大致可以理解為，你要構造一個1~n的全排列。題目給出你前k項，你要把剩下的構造出來。

規定1、從構造好的序列中，只能從第一個數按順序取

2、有一個棧可以暫時儲存數字。

遵照兩種規定，每次往數列b中放一個數，使得最終數列b是升序的。

【分析】

通過多組示例分析可以得出一些規律。

從全排列開頭開始取數字，這個數字x有三種去向

1.如果數列b的下一項恰好是x，那就讓x加入b

2.不滿足1時，考慮讓x先入棧儲存，但是x必須小於棧中任意元素，才能入棧。

3.不滿足1,2時，這個全排列是構造不出來的。

模擬這個過程操作前k項，然後開始考慮棧中剩餘數字。

棧中之所以有剩餘是因為數列b中沒有比他們小的數，那就從棧頂開始考慮，把小於棧頂的數加入b中。

執行完這一過程後，倒序把所有沒加入的數字加入到b中即可。

【程式碼】

#include<bits/stdc++.h>
using namespace std;
int sta[202020];
int a[202020];
bool vis[202020];
int n,k;
int main()
{
    while(cin>>n>>k)
    {
        memset(sta,0,sizeof(sta));
        memset(vis,0,sizeof(vis));
        int flag=1,b=0,top=0;
        for(int i=1;i<=k;i++)
        {
            int x;cin>>x;
            a[i]=x;
            vis[x]=1;
            if(x==b+1)//->b
                b++;
            else if(top==0||x<sta[top-1])
                sta[top++]=x;
            else flag=0;
            while(top&&sta[top-1]==b+1)
            {
                b++;top--;
            }
        }
        if(flag==0)
        {
            cout<<-1<<endl;
            continue;
        }
        for(int i=1;i<=k;i++)
            cout<<a[i]<<" ";
        sta[top]=0;
        for(int i=top-1;i>=0;i--)
        {
            for(int j=sta[i]-1;j>sta[i+1];j--)if(!vis[j])
            {
                cout<<j<<" ";
                vis[j]=1;
            }
        }
        for(int j=n;j;j--)if(!vis[j])
            cout<<j<<" ";
        cout<<endl;
    }
}