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}, …, 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].

inputFormat

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).

outputFormat

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].

样例

2 1 2
-1000000000 1000000000

0
1 

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