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 Ruby (2.3.3) (judge verdict: Runtime Error)

require 'forwardable'

class SumArray
  extend Forwardable
  
  def_delegator :@elements, :each

  def initialize
    @elements = []
  end
  
  def push(val, count)
    if @elements.empty?
      @elements << [val, count]
    else
      right = [*@elements.each_with_index].bsearch{ |x, _| x[0] > val }
      if right == nil
        @elements << [val, count]
      elsif right.last > 0
        if @elements[right.last - 1][0] == val
          @elements[right.last - 1][1] += count
        else
          @elements.insert(index, [val, count])
        end
      else
        @elements.insert(index, [val, count])
      end
    end
  end
end

n, k = gets.split.map(&:to_i)
sum_array = SumArray.new
n.times do
  a, b = gets.split.map(&:to_i)
  sum_array.push(a, b)
end

sum_array.each do |x|
  k -= x[1]
  if k <= 0
    puts x[0]
    exit
  end
end