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)

import Data.List (foldl')

parse1 :: IO Int
parse1 = getLine >>= return . read

parse2 :: IO [Double]
parse2 = getLine >>= return . fmap read . words

parse3 :: IO [Double]
parse3 = getLine >>= return . fmap read . words

type T = Double
type A = Double
type H = Double

calc :: T -> [H] -> [Double]
calc t hs = map calc' hs
  where calc' h = t - 0.006 * h

indexed :: [a] -> [(Int, a)]
indexed as = go 1 as
  where go i (x:xs) = (i, x) : go (i + 1) xs
        go _ _ = []

choose :: T -> A -> [H] -> Int
choose t a hs = 
  let ts = indexed $ calc t hs
  in fst $ foldr1 choose' ts
  where choose' :: (Int, Double) -> (Int, Double) -> (Int, Double)
        choose' (n, d) (n', d') = if abs(a - d) < abs(a - d')
                                  then (n, d)
                                  else (n', d')

main = do
  n <- parse1
  [t, a] <- parse2
  hs <- parse3
  print $ choose t a hs