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 C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;

class Program
{
    static void Main(string[] args)
    {
      var input = new InputC();
      var result = findK(input, input.K);
      Console.WriteLine(result);
    }

    static int findK(InputC ic, int k)
    {
      var index = 0;
      var lastA_i = ic.ABTuples.First.Value.a_i;
      // b_iを順番に足して行って、kを超えたらその直前の値を返す
      foreach(var tuple in ic.ABTuples)
      {
        if(index >= k)
        {
          return lastA_i;
        }
        else
        {
          index += tuple.b_i;
          lastA_i = tuple.a_i;
        }
      }
      return lastA_i;
    }

    class InputC
    {
      public int N {get; set;}
      public int K {get; set;}

      public LinkedList<ABTupleC> ABTuples {get;set;}
      public class ABTupleC
      {
        public int a_i {get; set;}
        public int b_i {get; set;}
      }

      public InputC()
      {
        var line0 = Console.ReadLine().Split(" ");
        this.N = int.Parse(line0[0]);
        this.K = int.Parse(line0[1]);
        this.ABTuples = new LinkedList<ABTupleC>();

        for(var i = 0; i < this.N; i++)
        {
          var line = Console.ReadLine().Split(" ");
          var newTuple = new ABTupleC()
          {
            a_i = int.Parse(line[0]),
            b_i = int.Parse(line[1]),
          };

          var found = false; // 
          foreach(var tuple in this.ABTuples)
          {
            if(newTuple.a_i < tuple.a_i)
            {
              // this.ABTuplesは小さい順に並んでいるから
              // 小さい方から挿入を試していくといずれnewTuple.a_i < tuple.a_i となるタイミングがあるはず
              this.ABTuples.AddBefore(
                this.ABTuples.Find(tuple),
                new LinkedListNode<ABTupleC>(newTuple)
              );
              found = true;
              break;
            }
            // newTuple.a_i > tuple.a_i の間は何もしない
          }

          if(!found)
          {
            // これまで追加されたa_iよりも大きい数字なら、最後尾に追加する
            this.ABTuples.AddLast(new LinkedListNode<ABTupleC>(newTuple));
          }

        }
      }
    }
}