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 <bits/stdc++.h>
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
using namespace std;
typedef long long ll;
typedef long double ld;
int n, a, b;
int main() {
	scanf("%d%d%d", &n, &a, &b);
	if(n < a + b - 1 || n > 1ll * a * b) { puts("-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;
	}
	for(int i=b; i>=1; i--) printf("%d ", i);
	int curr = b + 1;
	for(int i=0; i<a-1; i++) {
		int len = ((n - curr + 1) + a - i - 2) / (a - i - 1);
		for(int j=curr+len-1; j>=curr; j--) printf("%d ", j);
		curr += len;
	}
	return 0;
}