Codeforces 911E Stack Sorting （模拟）

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:

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.

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

题目链接：http://codeforces.com/contest/911/problem/E

题意：有n个数，其中k个数给定你入栈顺序（即数组a[]中存储的元素），剩余n-k个元素的输入顺序由你自己决定，使得n个元素的出栈顺序为升序。如果有多种答案，则输出入栈顺序字典序最大的一种。

#include <bits/stdc++.h>
using namespace std;

const int N = 2e5+10;
int n,k,a
,vis
,top,b
,num;

int main(){
scanf("%d%d",&n,&k);
for(int i = 0; i < k; i ++) scanf("%d",&a[i]);
num = 1;
for(int i = 0; i < k; i ++){
vis[a[i]] = 1;
b[++ top] = a[i];
while(top && b[top] == num) top --, num ++;
}
int flag = 0;
for(int i = 1; i < top; i ++){
if(b[i] < b[i+1]){
flag = 1; break;
}
}
if(flag) printf("-1\n");
else{
for(int i = 0; i < k; i ++){
if(i) printf(" ");
printf("%d",a[i]);
}
b[top+1] = num-1;
while(top > 0){
for(int i = b[top]-1; i > b[top+1]; i --) printf(" %d",i);
top --;
}
for(int i = n; i > b[top+1]; i --) printf(" %d",i);
printf("\n");
}
return 0;
}