Description
\(N\) people are sitting in a circular hot tub, labeled \(1\) to \(N\) in clockwise order. A scalding wave of bathwater starts at person \(1\) with an initial strength \(K\). The wave travels \(K\) steps circularly. (If \(K\) is positive, the wave moves clockwise; if \(K\) is negative, it moves counter-clockwise).
The person the wave lands on passes out from the extreme heat and is dragged out immediately. Upon their removal, the next wave starts from the person immediately following the fainted individual (in the direction of the previous wave’s travel). The strength of this next wave, \(S\), is equal to the heat tolerance \(T_i\) of the person who just fainted.
This process continues until only one person remains in the tub.
Input
- Line 1: Two integers: \(N\) (the number of people) and \(K\) (the initial wave strength).
- Line 2: \(N\) non-zero integers \(T_1, T_2, \dots, T_N\) representing the heat tolerances of each person
Constraints:
- \(2 \le N \le 10^5\)
- \(-10^9 \le K, T_i \le 10^9\)
- \(K, T_i \neq 0\)
Output
- Line 1: The labels of the people in the order they are removed, each with one space.
- Line 2: The label of the final survivor with '\n'.