Problem: An array b is called to be a subarray of a if it forms a continuous subsequence of a, that is, if it is equal to a_l, a_{l + 1}, …, a_r for some l, r.

Suppose m is some known constant. For any array, having m or more elements, let's define it's beauty as the sum of m largest elements of that array. For example: 

  * For array x = [4, 3, 1, 5, 2] and m = 3, the 3 largest elements of x are 5, 4 and 3, so the beauty of x is 5 + 4 + 3 = 12.
  * For array x = [10, 10, 10] and m = 2, the beauty of x is 10 + 10 = 20.



You are given an array a_1, a_2, …, a_n, the value of the said constant m and an integer k. Your need to split the array a into exactly k subarrays such that:

  * Each element from a belongs to exactly one subarray.
  * Each subarray has at least m elements.
  * The sum of all beauties of k subarrays is maximum possible.

Input

The first line contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m, 2 ≤ k, m ⋅ k ≤ n) — the number of elements in a, the constant m in the definition of beauty and the number of subarrays to split to.

The second line contains n integers a_1, a_2, …, a_n (-10^9 ≤ a_i ≤ 10^9).

Output

In the first line, print the maximum possible sum of the beauties of the subarrays in the optimal partition.

In the second line, print k-1 integers p_1, p_2, …, p_{k-1} (1 ≤ p_1 < p_2 < … < p_{k-1} < n) representing the partition of the array, in which:

  * All elements with indices from 1 to p_1 belong to the first subarray.
  * All elements with indices from p_1 + 1 to p_2 belong to the second subarray.
  * ….
  * All elements with indices from p_{k-1} + 1 to n belong to the last, k-th subarray.



If there are several optimal partitions, print any of them.

Examples

Input


9 2 3
5 2 5 2 4 1 1 3 2


Output


21
3 5 

Input


6 1 4
4 1 3 2 2 3


Output


12
1 3 5 

Input


2 1 2
-1000000000 1000000000


Output


0
1 

Note

In the first example, one of the optimal partitions is [5, 2, 5], [2, 4], [1, 1, 3, 2].

  * The beauty of the subarray [5, 2, 5] is 5 + 5 = 10. 
  * The beauty of the subarray [2, 4] is 2 + 4 = 6. 
  * The beauty of the subarray [1, 1, 3, 2] is 3 + 2 = 5. 



The sum of their beauties is 10 + 6 + 5 = 21.

In the second example, one optimal partition is [4], [1, 3], [2, 2], [3].

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;

public class Temp3
{	
	public static void main(String[] args) throws NumberFormatException, IOException 
	{
		Scanner obj = new Scanner(System.in);
		int n = obj.nextInt();
		int m = obj.nextInt();
		int k = obj.nextInt();
		int[] arr = new int[n];
		PriorityQueue<Pair> pq = new PriorityQueue<>(new Pair());
		for(int i=0 ; i<n ; i++)
		{
			arr[i] = obj.nextInt();
			pq.add(new Pair(arr[i], i));
		}
		
		long sum = 0;
		int indices[] = new int[m*k];
		
		for(int i=0 ; i<m*k ; i++)
		{
			Pair temp = pq.remove();
			sum += temp.element;
			indices[i] = temp.index;
		}
		
		Arrays.sort(indices);
		System.out.println(sum);
		int i = m-1;
		int count = 0;
		while(count != k-1)
		{
			System.out.print((indices[i]+1) + " ");
			i += m;
			count++;
		}
		System.out.println();
	}
}

class Pair implements Comparator<Pair>
{
	int element;
	int index;
	
	Pair()
	{
		
	}
	
	Pair(int element, int index)
	{
		this.element = element;
		this.index = index;
	}

	@Override
	public int compare(Pair o1, Pair o2) 
	{
		return o2.element - o1.element;
	}
}