Longest Subsequence

Description:

Input:

The first line contains two integers n and m (1 ≤ n, m ≤ 10⁶) — the size of the array a and the parameter from the problem statement.

The second line contains n integers a_i (1 ≤ a_i ≤ 10⁹) — the elements of a.

Output:

In the first line print two integers l and k_max (1 ≤ l ≤ m, 0 ≤ k_max ≤ n) — the value of LCM and the number of elements in optimal subsequence.

In the second line print k_max integers — the positions of the elements from the optimal subsequence in the ascending order.

Note that you can find and print any subsequence with the maximum length.

Sample Input:

7 8
6 2 9 2 7 2 3

Sample Output:

6 5
1 2 4 6 7

Sample Input:

6 4
2 2 2 3 3 3

Sample Output:

2 3
1 2 3