Since beginning her university studies, Ava has been going to a nearby plaza for lunch. In order to maintain good eating habits throughout her university career, Ava has crafted a perfect dining strategy.

Ava began by eating at each of the ~N~ restaurants (numbered ~1~ through ~N~) at the plaza and rating how much she enjoyed the food. Once she gathered all the ratings, she would only eat at the highest-rated restaurant. (If there is a tie, she eats at the lowest-numbered restaurant.) However, after a week of eating the same food, Ava realized she needs more variety in her diet. To fix this issue, she decided that eating at a restaurant would cause its rating to drop by a fixed amount, ~M~.

Armed with her dining strategy, Ava wonders where she will grab lunch on her last day of university, which is ~K~ days away if she eats at exactly one restaurant per day.

Input Specification

The input contains ~10~ test cases. Each test case starts with three integers ~N, M~ ~(1 \le N, M \le 10^5)~, ~K~ ~(1 \le K \le 10^{12})~. The next line contains ~N~ positive integers ~R_p~ ~(1 \le R_p \le 10^9)~, where ~R_p~ represents the rating of the ~p^{th}~ restaurant at the plaza. Restaurants are numbered starting from ~1~.

For the first four test cases in the file, ~N \cdot K \le 10^6~. For the first seven cases, ~K \le 10^6~.

Output Specification

For each test case, your program should output one integer representing the restaurant Ava will eat at on the ~K^{th}~ day.

Sample Input

2 5 4
20 17
5 4 7
1 2 4 8 16
4 8 100
3 22 20 14

Sample Output

2
5
3

Note: Only ~3~ cases are shown in this sample.

Educational Computing Organization of Ontario - statements, test data and other materials can be found at ecoocs.org