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 OCaml (4.02.3) (judge verdict: Accepted)

let () = Scanf.scanf "%d %d\n" @@ fun n k ->
    let a =
        Array.init n @@ fun _ -> Scanf.scanf "%d %d\n" @@ fun a b -> (a, b) in
    Array.sort (fun (x, _) (y, _) -> x - y) a;
    let rec f acc i =
        if (snd a.(i)) + acc >= k then fst a.(i) else f ((snd a.(i)) + acc) (i+1)
    in f 0 0 |> Printf.printf "%d"