Problem:
Score : 300 points

Problem Statement

There is an empty array.
The following N operations will be performed to insert integers into the array.
In the i-th operation (1≤i≤N), b_i copies of an integer a_i are inserted into the array.
Find the K-th smallest integer in the array after the N operations.
For example, the 4-th smallest integer in the array \{1,2,2,3,3,3\} is 3.

Constraints

1≤N≤10^5

1≤a_i,b_i≤10^5

1≤K≤b_1…+…b_n

All input values are integers.

Input

Input is given from Standard Input in the following format:

N K
a_1 b_1
:
a_N b_N

Output

Print the K-th smallest integer in the array after the N operations.

Sample Input 1

3 4
1 1
2 2
3 3

Sample Output 1

3

The resulting array is the same as the one in the problem statement.

Sample Input 2

10 500000
1 100000
1 100000
1 100000
1 100000
1 100000
100000 100000
100000 100000
100000 100000
100000 100000
100000 100000

Sample Output 2

1

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Prelude hiding (abs)
import Control.Monad
import Control.Arrow ((&&&))
import Data.List (nub, sort, group, find)
import Data.Maybe (fromMaybe, fromJust)
import qualified Data.IntMap as M

type Counter = M.IntMap Int

main :: IO ()
main = do
    [n, k] <- (map read . words) <$> getLine
    abs <- map readLine2 <$> replicateM n getLine
    print $ solve abs k

-- |
--
-- >>> solve [(1,1),(2,2),(3,3)] 4
-- 3
solve :: [(Int,Int)] -> Int -> Int
solve abs k = fst y
  where
    c = foldl update M.empty abs
    y = head . dropWhile (\(_,b) -> b < k) $ scanl f (0,0) (sort $ M.assocs c)
    f (a1,b1) (a2,b2) = (a2, b1 + b2)

update :: Counter -> (Int,Int) -> Counter
update c (a,b) = M.insertWith (+) a b c

readLine2 :: String -> (Int,Int)
readLine2 = tuplify2 . map read . words
    where
      tuplify2 [] = (0, 0)
      tuplify2 [x] = (x, 0)
      tuplify2 (x:y:_) = (x, y)