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;
#define REP(i,st,ed) for(register int i=st,i##end=ed;i<=i##end;++i)
#define DREP(i,st,ed) for(register int i=st,i##end=ed;i>=i##end;--i)
typedef long long ll;
inline int read(){
	int x;
	char c;
	int f=1;
	while((c=getchar())!='-' && (c<'0' || c>'9'));
	if(c=='-') c=getchar(),f=-1;
	x=c^'0';
	while((c=getchar())>='0' && c<='9') x=(x<<1)+(x<<3)+(c^'0');
	return x*f;
}
inline ll readll(){
	ll x;
	char c;
	ll f=1;
	while((c=getchar())!='-' && (c<'0' || c>'9'));
	if(c=='-') c=getchar(),f=-1;
	x=c^'0';
	while((c=getchar())>='0' && c<='9') x=(x<<1ll)+(x<<3ll)+(c^'0');
	return x*f;
}
const int maxn=3e5+10;
int a[maxn];
int main(){
	int n=read(),A=read(),B=read();
	if(A*B<n  || A+B-1>n || A>n || B>n || A<1 || B<1){
		printf("-1\n");
		return 0;
	}
	int tmp=0,res=n;
	REP(i,res-A+1,res) printf("%d ",i);
	res=res-A;
	int x=0;
	if(res) x=res/(B-1);
	B--;
	while(res){
		int u=res-x+1;
		if(B*x<res) u--;
		REP(i,u,res) printf("%d ",i);
		B--;
		res=u-1;
	}
	return 0;
}