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 Control.Monad.ST
import qualified Data.ByteString.Char8 as C
import Data.List
import Data.Maybe
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM

main = sol <$> get >>= print

get = fmap (unfoldr (C.readInt . C.dropWhile (==' '))) . C.lines <$> C.getContents  
 
sol ([_,k]:ab) = fromJust . U.findIndex (k<=) . U.scanl1' (+) $ runST $ do
  v <- UM.replicate (1+10^5 :: Int) (0 :: Int)
  forM_ ab $ \[a,b] -> UM.modify v (+b) a
  U.freeze v