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)

data = []
now_k = nil

N.times do
  a,b = gets.split.map &:to_i

  flag = true
  len = 0

  data.each_with_index do |d, i|
    if now_k && now_k < d[0]
      flag = false
      break
    end

    # K番目の値を保持してそれより大きかったら終了

    if d[0] == a
      d[1] += b
      flag = false
    elsif a < d[0]
      data.insert(i, [a,b])
      flag = false
    end

    len += d[1]
    if K <= len
      now_k = d[0]
      flag = false
    end

    unless flag
      break
    end
  end

  data << [a,b] if flag
end

# warn data

len = 0
data.each do |(v, n)|
  len += n
  if K <= len
    puts v
    break
  end
end