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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE BangPatterns, MultiWayIf #-}

import Control.Applicative
import Control.Monad
import Data.List
import Debug.Trace (traceShow, traceShowM)

import Data.Ord (comparing)

solve :: Int -> Int -> Int -> [Double] -> Int
solve n t a hs = fst . head $ sortBy (comparing snd) $ zip [1..] qs
  where
    ps = fmap (\h -> fromIntegral t - h * 0.006) hs
    qs = fmap (abs . subtract (fromIntegral a)) ps

main :: IO ()
main = do
    n <- readLn :: IO Int
    [t, a] <- fmap read . words <$> getLine
    hs <- fmap read . words <$> getLine
    print $ solve n t a hs