B. Yet Another Array Partitioning Tasktime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAn 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.InputThe 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).OutputIn 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.ExamplesInput
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 NoteIn 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].
9 2 3
5 2 5 2 4 1 1 3 2

21 3 5 
['constructive algorithms', 'greedy', 'sortings', '*1500']