Problem:
Score: 200 points

Problem Statement

A country decides to build a palace.

In this country, the average temperature of a point at an elevation of x meters is T-x \times 0.006 degrees Celsius.

There are N places proposed for the place. The elevation of Place i is H_i meters.

Among them, Princess Joisino orders you to select the place whose average temperature is the closest to A degrees Celsius, and build the palace there.

Print the index of the place where the palace should be built.

It is guaranteed that the solution is unique.

Constraints

1 \leq N \leq 1000

0 \leq T \leq 50

-60 \leq A \leq T

0 \leq H_i \leq 10^5

All values in input are integers.

The solution is unique.

Input

Input is given from Standard Input in the following format:

N
T A
H_1 H_2 ... H_N

Output

Print the index of the place where the palace should be built.

Sample Input 1

2
12 5
1000 2000

Sample Output 1

1

The average temperature of Place 1 is 12-1000 \times 0.006=6 degrees Celsius.

The average temperature of Place 2 is 12-2000 \times 0.006=0 degrees Celsius.

Thus, the palace should be built at Place 1.

Sample Input 2

3
21 -11
81234 94124 52141

Sample Output 2

3

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {
    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        int T = scanner.nextInt();
        double A = (double) scanner.nextInt();

        Map<Integer, Double> map = new TreeMap<>();

        for (int i = 0; i < N; i++) {
            map.put(i + 1, Math.abs(A - (T - (scanner.nextInt() * 0.006))));
        }

        System.out.println(map.entrySet().stream().sorted(Map.Entry.comparingByValue()).findFirst().get().getKey());
    }
}