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)

main = do
    _ <- getLine
    line <- getLine
    line2 <- getLine
    let (x : y : _) = map read . words $ line
    let hs = map read . words $ line2
    putStrLn . show $ solve x y hs

-- |
-- >>> solve 12 5 [1000, 2000]
-- 1
-- >>> solve 21 (-11) [81234, 94124, 52141]
-- 3

solve :: Int -> Int -> [Int] -> Int
solve t a (h:hs) = fst . foldl min' (1, (1, delta h)) $ hs
    where
        temp h' = (realToFrac t) - (realToFrac h') * 0.006
        delta h'' = abs (realToFrac a - temp h'')
        min' (xa, (xb, xc)) y
            | xc < delta y = (xa, (xb + 1, xc))
            | otherwise   = (xb + 1, (xb + 1, delta y))