An array is given, and an index present in it.

A window must be chosen such that it includes the index, has this component maximized — sum(a[i]...a[j])*(j-i+1), but the component must be equal to or less than the threshold (sum(a[i]...a[j])*(j-i+1) <= threshold).

How we can solve this question optimally?

One example of the problem:

Input

N: 8

Arr[]: [2,-3,-4,5,5,6,7,8]

Ind: 4

Threshold = 20

Output

One possible answer [5,5]

Explanation of output [5, 5] = 10*2 = 20 <= 20 (threshold)