Problem: 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.

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.

Examples

Input

5 3 2


Output

2 4 1 5 3


Input

7 7 1


Output

1 2 3 4 5 6 7


Input

300000 300000 300000


Output

-1

Solution (in CPP):

Solution:
#include <cstdio>
using namespace std;
int cnt[300006];
int main(){
	register int n, a, b, i, j, sum;
	scanf("%d %d %d", &n, &a, &b);
	if ((n + a - 1) / a > b || b + a > n + 1) {
		puts("-1");
		return 0;
	}
	if (a == 1) {
		for (i = n; i; --i) printf("%d ", i);
	}
	else {
		cnt[1] = b;
		for (i = b + 1; i <= n; ++i) ++cnt[i % (a - 1) + 2];
		sum = 0;
		for (i = 1; i <= a; ++i) {
			sum += cnt[i];
			for (j = 0; j < cnt[i]; ++j) printf("%d ", sum - j);
		}
	}
	return 0;
}