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<algorithm>
#include<cctype>
#include<cmath>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<map>
#include<queue>
#include<stack>
#include<vector>
#define size 500010
#define debug(x) cerr<<#x<<"="<<x
#define gc getchar()
#define db double
#define ll long long
#define rep(i,s,n) for (register int i=s;i<=n;i++)
#define drep(i,n,s) for (register int i=n;i>=s;i--)
#define il inline
using namespace std;

il ll r()
{
	char c; ll x,f=1;
	for (c=gc;!isdigit(c);c=gc) if (c=='-') f=-1; x=c-'0';
	for (c=gc;isdigit(c);c=gc) x=(x<<1)+(x<<3)+c-'0';
	return f*x;
}

ll n,perm[size],a,b,len[size];

int main()
{
	n=r(); a=r(); b=r();
	if (a*b<n||a+b>n+1) {cout<<-1<<endl;return 0;}
	rep(i,1,a) cout<<n+i-a<<' '; n-=a,b--;
	if (!b) return 0;
	ll bl=n/b; rep(i,1,b) len[i]=bl;
	rep(i,1,n%b) len[i]++;
	rep(i,1,b)
	{
		rep(j,n-len[i]+1,n) cout<<j<<' ';
		n-=len[i];
	}  
	return 0;
}