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Contest: Task: Related: TaskA TaskC

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