Problem:
Score : 700 points

Problem Statement

Determine if there exists a sequence obtained by permuting 1,2,...,N that satisfies the following conditions:

The length of its longest increasing subsequence is A.

The length of its longest decreasing subsequence is B.

If it exists, construct one such sequence.

Notes

A subsequence of a sequence P is a sequence that can be obtained by extracting some of the elements in P without changing the order.

A longest increasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically increasing.

Similarly, a longest decreasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically decreasing.

Constraints

1 \leq N,A,B \leq 3\times 10^5

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

If there are no sequences that satisfy the conditions, print -1.

Otherwise, print N integers. The i-th integer should be the i-th element of the sequence that you constructed.

Sample Input 1

5 3 2

Sample Output 1

2 4 1 5 3

One longest increasing subsequence of this sequence is {2,4,5}, and one longest decreasing subsequence of it is {4,3}.

Sample Input 2

7 7 1

Sample Output 2

1 2 3 4 5 6 7

Sample Input 3

300000 300000 300000

Sample Output 3

-1

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include<cmath>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<iomanip>
#define sqr(x) (x)*(x)
using namespace std;
int n,m,x,y,i,j,ans[300005],ss[300005];
bool check()
{
	vector<int> a,b;
	int i;
//	cerr<<endl;
	for (i=1;i<=n;i++)
	{
		if (a.empty()||a.back()<ans[i]) a.push_back(ans[i]); else *(upper_bound(a.begin(),a.end(),ans[i]))=ans[i];
		if (b.empty()||b.back()<-ans[i]) b.push_back(-ans[i]); else *(upper_bound(b.begin(),b.end(),-ans[i]))=-ans[i];
//		cerr<<a.size()<<' '<<b.size()<<endl;
//		cerr<<a.back()<<' '<<b.back()<<endl;
	}
	return a.size()==x&&b.size()==y;
}
void print()
{
	for (i=1;i<=n;i++) cout<<ans[i]<<' ';
}
int main()
{
	ios_base::sync_with_stdio(0);
	cin>>n>>x>>y;
	if (x+y-1>n)
	{
		cout<<-1;
		return 0;
	}
	if (x+y-1==n)
	{
		for (i=1;i<x;i++) cout<<i<<' ';
		for (i=n;i>=x;i--) cout<<i<<' ';
		return 0;
	}
	if (x==1)
	{
		cout<<-1;
		return 0;
	}
	if (y==1)
	{
		cout<<-1;
		return 0;
	}
	int a,cnt,b,c,bck;
	a=n+1-x-y;b=y-1;c=x;cnt=0;
	for (i=a+b+1;i<=n;i++) ans[i]=++cnt;
	for (i=1;i<=a;i++) ans[i]=++cnt;
	for (i=a+b;i>a;i--) ans[i]=++cnt;
	if (check()){print();return 0;}
	a=n+1-x-y;b=x-1;c=y;cnt=0;
	for (i=a+1;i<=a+b;i++) ans[i]=++cnt;
	for (i=a;i;i--) ans[i]=++cnt;
	for (i=n;i>a+b;i--) ans[i]=++cnt;
	if (check()){print();return 0;}
	a=x-2;b=y;c=n+2-x-y;cnt=0;
	for (i=1;i<=a;i++) ans[i]=++cnt;
	for (i=a+b;i>a;i--) ans[i]=++cnt;
	for (i=n;i>a+b;i--) ans[i]=++cnt;
	a=x-2;b=y;c=n+2-x-y;cnt=0;
	for (i=1;i<=a;i++) ans[i]=++cnt;
	for (i=a+b;i>a;i--) ans[i]=++cnt;
	for (i=n;i>a+b;i--) ans[i]=++cnt;
	if (check()){print();return 0;}
	a=n+1-x-y;b=y;c=x-1;cnt=0;
	for (i=a+b+1;i<=n;i++) ans[i]=++cnt;
	for (i=1;i<=a;i++) ans[i]=++cnt;
	for (i=a+b;i>a;i--) ans[i]=++cnt;
	if (check()){print();return 0;}
	a=n+1-x-y;b=x;c=y-1;cnt=0;
	for (i=a+1;i<=a+b;i++) ans[i]=++cnt;
	for (i=a;i;i--) ans[i]=++cnt;
	for (i=n;i>a+b;i--) ans[i]=++cnt;
	if (check()){print();return 0;}
	cnt=0;bck=0;
	//for (j=min(n,i+y-1);j>=i;j--) ans[j]=++cnt;
	memset(ss,0,sizeof(ss));
	for (i=1;i<=n;i+=y)
	{
		bck++;
		for (j=min(n,i+y-1);j>=i;j--) ss[bck]++;
	}
	int i=1;
	while (bck<x)
	{
		if (i>bck) break;
		if (ss[i]>1)
		{
			ss[i]--;
			bck++;
			ss[bck]=1;
		}
		else i++;
	}
	for (i=1;i<=n;i+=ss[bck+1])
	{
		for (j=min(n,i+ss[bck]-1);j>=i;j--) ans[j]=++cnt;
		bck--;
	}
	if (check()){print();return 0;}
	/*cnt=0;
	for (i=n;i>=0;i-=x)
	{
		for (j=max(1,i-x+1);j<=i;j++) ans[j]=++cnt;
	}
	if (check()){print();return 0;}*/
	/*b=y-1;c=x;
	if (a+1<=x)
	{
		for (i=a+b+1;i<=n;i++) ans[i]=++cnt;
		for (i=1;i<=a;i++) ans[i]=++cnt;
		for (i=a+b;i>a;i--) ans[i]=++cnt;
		for (i=1;i<=n;i++) cout<<ans[i]<<' ';
		return 0;
	}
	b=x-1;c=y;
	if (a+1<=y)
	{
		for (i=a+1;i<=a+b;i++) ans[i]=++cnt;
		for (i=a;i;i--) ans[i]=++cnt;
		for (i=n;i>a+b;i--) ans[i]=++cnt;
		for (i=1;i<=n;i++) cout<<ans[i]<<' ';
		return 0;
	}*/
	cout<<-1;
	return 0;
}