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: Time Limit Exceeded)

N,K=gets.split.map &:to_i
as=N.times.map {gets.split.map(&:to_i)}

arr=Array.new(as[0][1],as[0][0])
(1...N).each do |i|
  idx=arr.bsearch_index{|x|as[i][0]<=x}

  if idx.nil?
    arr=arr+Array.new(as[i][1],as[i][0])
  else
    arr=arr[0..idx]+Array.new(as[i][1],as[i][0])+arr[idx..-1]
  end
end
p arr[K-1]