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.

2
12 5
1000 2000

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 $1$.

3
21 -11
81234 94124 52141

3