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: Wrong Answer)

#include<bits/stdc++.h>
#define ll long long
using namespace std;
void qmax(int &x,int y) {if (x<y) x=y;}
void qmin(int &x,int y) {if (x>y) x=y;}
inline int read()
{
	char s;
	int k=0,base=1;
	while((s=getchar())!='-'&&s!=EOF&&!(isdigit(s)));
	if(s==EOF)exit(0);
	if(s=='-')base=-1,s=getchar();
	while(isdigit(s)){k=k*10+(s^'0');s=getchar();}
	return k*base;
}
inline void write(int x)
{
	static char cnt,num[15];cnt=0;
	if (!x)
	{
		putchar('0');
		return;
	}
	for (;x;x/=10) num[++cnt]=x%10;
	for (;cnt;putchar(num[cnt--]+48));
}
const int maxn=3e5+100;
ll n,a,b;
int c[maxn],s,cnt,k,id;
int main()
{
#ifdef ylx
	freopen("arc91c.in","r",stdin);
	freopen("arc91c.out","w",stdout);
#endif
	n=read();a=read();b=read();
	if (a+b>n+1)
	{
		printf("-1");
		return 0;
	}
	if (a*b<n)
	{
		printf("-1");
		return 0;
	}
	if (a==1)
	{
		for (int i=n;i>=1;i--) printf("%d ",i);
		return 0;
	}
	if (b==1)
	{
		for (int i=1;i<=n;i++) printf("%d ",i);
		return 0;
	}
	int aa=0;
	s=(n-a+1)/(b);
	for (int i=1;i<=a;i++)
	{
		if (s>0)
		{
			k=b*i+1;
			while (k>b*(i-1)+1)
			{
				k--;
				id++;
				c[id]=k;
			}
			aa++;
			s--;
		}
		if (s==0)
		{
			aa=(int)a-aa;
			int ID=id;
			for (int j=ID+1;j<=min((int)n,ID+aa);j++)
			{
				id++;
				c[id]=j;
			}
			for (int j=id+1;j<=n;j++)
			{
				id++;
				c[id]=j;
			}
			break;
		}
	}
	for (int i=1;i<=n;i++) printf("%d ",c[i]);
	return 0;
}