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 Control.Monad
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
main = do
  [n,k] <- map read . words <$> getLine :: IO [Int]
  xs <- map (\[a,b] -> (a,b)) . map (map read . words) . lines <$> getContents :: IO [(Int,Int)]
  let v = vec xs
  print $ solve v 1 k

vec :: [(Int,Int)] -> VU.Vector Int
vec xs = 
  VU.create $ do
    vec <- VUM.replicate (10^5+1) (0::Int)
    forM_ xs $ \(a,b) -> do
      r <- VUM.read vec a
      VUM.write vec a (b+r)
    return vec

solve :: VU.Vector Int -> Int -> Int -> Int
solve vec n k
  | b >= k = n
  | otherwise = solve vec (n+1) (k-b)
    where
      b = vec VU.! n