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
import Data.Ratio

main :: IO ()
main = do
  _ <- getLine
  [t, a] <- readInts
  hs <- readInts
  print $ solve t a hs

readInts :: IO [Int]
readInts = map read . words <$> getLine

solve :: Int -> Int -> [Int] -> Int
solve t a = fst . foldl1' f . zip [1..]
  where
    f (i, hi) (j, hj)
      | abs(averageTemp t hi - a % 1) < abs(averageTemp t hj - a % 1) = (i, hi)
      | otherwise                                                     = (j, hj)

averageTemp :: Int -> Int -> Ratio Int
averageTemp t x = t % 1 - x * 6 % 1000