CF1114B.Yet Another Array Partitioning Task

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 $a_l$ , $a_{l + 1}$ , $\ldots$ , $a_r$ 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 $a_1, a_2, \ldots, a_n$ , 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.

The first line contains three integers $n$ , $m$ and $k$ ( $2 \le n \le 2 \cdot 10^5$ , $1 \le m$ , $2 \le k$ , $m \cdot k \le n$ ) — 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 $a_1, a_2, \ldots, a_n$ ( $-10^9 \le a_i \le 10^9$ ).

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 $p_1, p_2, \ldots, p_{k-1}$ ( $1 \le p_1 < p_2 < \ldots < p_{k-1} < n$ ) 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.
• $\ldots$ .
• 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.

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 $[4]$ , $[1, 3]$ , $[2, 2]$ , $[3]$ .