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: Runtime Error)

#include <cstdio>

using namespace std;

#define REP(i,n)   for(int i=0; i<(int)(n); i++)
#define FOR(i,b,e) for(int i=(b); i<=(int)(e); i++)

const int N_MAX = 300000;

int N, A, B;
int a[N_MAX];

void solve() {
  if (A + B > N + 1) {
    puts("-1");
    return;
  }
  if (A * B < N) {
    puts("-1");
    return;
  }
  REP(i, A) REP(j, B) {
    int k = i * B + j;
    if (k >= N) break;
    a[i * B + j] = j * A + i + 1;
  }

  REP(i, N) printf("%d%c", a[i], i + 1 == N ? '\n' : ' ');
}

void input() {
  scanf("%d%d%d", &N, &A, &B);
}

int main() {
  input();
  solve();
  return 0;
}