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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defun read-list-from-string (str)
  (read-from-string (concatenate 'string "(" str ")")))

(defun read-num-from-string (str)
  (parse-integer str))

(defun read-list ()
  (read-list-from-string (read-line)))

(defun read-as-table (num)
  (let ((table nil)
	(lists (loop repeat num
		     for e = (read-list) then (read-list)
		     collect (cons (car e) (cadr e)))))
    (dolist (e (sort lists (lambda (x y) (<= (car x) (car y)))) (reverse table))
      (if (and table (= (caar table) (car e)))
	    (incf (cdar table) (cdr e))
	    (push e table)))))

(defun get-nth-min (num sorted)
  (let ((sorted (sort alist )))
    (labels ((inner-loop (rest acc)
	       (if (>= (+ acc (cdar rest)) num)
		   (caar rest)
		   (inner-loop (cdr rest) (+ acc (cdar rest))))))
      (inner-loop sorted 0))))

(defun solve ()
  (let* ((list (read-list))
	 (num (car list))
	 (limit (cadr list)))
    (princ (get-nth-min limit (read-as-table num)))
    (fresh-line)))

(solve)