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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.stream.IntStream;

/**
 * 解説どおりの計算方法で実装
 */
public class Main {

	/** 平均気温の係数 */
	private static final int D = 6;

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt(), t = scanner.nextInt() * 1000, a = scanner.nextInt() * 1000;
			Queue<Data> queue = new PriorityQueue<>();
			IntStream.range(0, n).forEach(i -> {
				int h = scanner.nextInt();
				queue.add(new Data(i + 1, Math.abs(t - h * D - a)));
			});
			System.out.println(queue.peek().index);
		}
	}

	/**
	 * 番号と平均気温を表すクラス
	 */
	private static class Data implements Comparable<Data> {
		/** 番号 */
		int index;
		/** 平均気温 */
		double t;

		Data(int index, double t) {
			super();
			this.index = index;
			this.t = t;
		}

		@Override
		public int compareTo(Data data) {
			return Double.compare(t, data.t);
		}
	}
}