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>
using namespace std;

int read()
{
	int ans=0;
	char ch=getchar();
	for(;(ch<'0' || ch>'9') && ch!='-';ch=getchar());
	bool flag=false;
	if(ch=='-')
	{
		flag=true;
		ch=getchar();
	}
	for(;ch>='0' && ch<='9';ch=getchar())ans=ans*10+ch-'0';
	return flag?-ans:ans;
}

long long rell()
{
	long long ans=0;
	char ch=getchar();
	for(;(ch<'0' || ch>'9') && ch!='-';ch=getchar());
	bool flag=false;
	if(ch=='-')
	{
		flag=true;
		ch=getchar();
	}
	for(;ch>='0' && ch<='9';ch=getchar())ans=ans*10ll+(long long)(ch-'0');
	return flag?-ans:ans;
}

void write(int a)
{
	if(!a)
	{
		putchar('0');
		return;
	}
	static char ans[233];
	int n=0;
	for(;a;a/=10)ans[n++]=a%10+'0';
	for(;n;)putchar(ans[--n]);
}

void write(long long a)
{
	if(!a)
	{
		putchar('0');
		return;
	}
	static char ans[233];
	int n=0;
	for(;a;a/=10)ans[n++]=a%10+'0';
	for(;n;)putchar(ans[--n]);
}

int main()
{
	int n,x,y;
	scanf("%d%d%d",&n,&x,&y);
	if(x+y>n+1 || (long long)x*y<n)
	{
		puts("-1");
		return 0;
	}
	for(int i=n,j;i;i=j-1)
	{
		j=i-i/y+1;
		y--;
		for(int k=j;k<=i;k++)printf("%d ",k);
	}
	puts("");
	return 0;
}