Problem:
Score : 300 points

Problem Statement

A programming competition site AtCode provides algorithmic problems.
Each problem is allocated a score based on its difficulty.
Currently, for each integer i between 1 and D (inclusive), there are p_i problems with a score of 100i points.
These p_1 + … + p_D problems are all of the problems available on AtCode.

A user of AtCode has a value called total score.
The total score of a user is the sum of the following two elements:

Base score: the sum of the scores of all problems solved by the user.

Perfect bonuses: when a user solves all problems with a score of 100i points, he/she earns the perfect bonus of c_i points, aside from the base score (1 ≤ i ≤ D).

Takahashi, who is the new user of AtCode, has not solved any problem.
His objective is to have a total score of G or more points.
At least how many problems does he need to solve for this objective?

Constraints

1 ≤ D ≤ 10

1 ≤ p_i ≤ 100

100 ≤ c_i ≤ 10^6

100 ≤ G

All values in input are integers.

c_i and G are all multiples of 100.

It is possible to have a total score of G or more points.

Input

Input is given from Standard Input in the following format:

D G
p_1 c_1
:
p_D c_D

Output

Print the minimum number of problems that needs to be solved in order to have a total score of G or more points. Note that this objective is always achievable (see Constraints).

Sample Input 1

2 700
3 500
5 800

Sample Output 1

3

In this case, there are three problems each with 100 points and five problems each with 200 points. The perfect bonus for solving all the 100-point problems is 500 points, and the perfect bonus for solving all the 200-point problems is 800 points. Takahashi's objective is to have a total score of 700 points or more.

One way to achieve this objective is to solve four 200-point problems and earn a base score of 800 points. However, if we solve three 100-point problems, we can earn the perfect bonus of 500 points in addition to the base score of 300 points, for a total score of 800 points, and we can achieve the objective with fewer problems.

Sample Input 2

2 2000
3 500
5 800

Sample Output 2

7

This case is similar to Sample Input 1, but the Takahashi's objective this time is 2000 points or more. In this case, we inevitably need to solve all five 200-point problems, and by solving two 100-point problems additionally we have the total score of 2000 points.

Sample Input 3

2 400
3 500
5 800

Sample Output 3

2

This case is again similar to Sample Input 1, but the Takahashi's objective this time is 400 points or more. In this case, we only need to solve two 200-point problems to achieve the objective.

Sample Input 4

5 25000
20 1000
40 1000
50 1000
30 1000
1 1000

Sample Output 4

66

There is only one 500-point problem, but the perfect bonus can be earned even in such a case.

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

;; -*- coding:utf-8 -*-

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 1))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))))

(defmacro print-line (obj &optional (stream '*standard-output*))
  `(prog1 (princ ,obj ,stream) (terpri ,stream)))


;; Hauptteil

(defmacro split-and-bind (arg-lst string &body body)
  (let ((pos1 (gensym "POS"))
	(pos2 (gensym "POS"))
	(str-evaled (gensym "STR")))
    (labels ((expand (arg-lst &optional (init-pos1 t))
	       (if (null arg-lst)
		   body
		   `((let* ((,pos1 ,(if init-pos1 0 `(1+ ,pos2)))
			    (,pos2 (position #\space ,str-evaled :start ,pos1 :test #'char=))
			    (,(car arg-lst) (parse-integer ,str-evaled :start ,pos1 :end ,pos2)))
		       ,@(expand (cdr arg-lst) nil))))))
      `(let ((,str-evaled ,string))
	 ,@(expand arg-lst)))))

(deftype uint nil `(integer 0 ,(expt 10 9)))
(defstruct problem
  i p c)
(defun get-complete-score (prob)
  (+ (* 100 (problem-i prob) (problem-p prob))
     (problem-c prob)))

(defun main ()
  (let* ((d (read))
         (g (read))
         (problem-lst
           (sort (loop for i from 1 to d
                       collect (split-and-bind (p c) (read-line)
                                 (make-problem :i i :p p :c c)))
                 #'>=
                 :key #'(lambda (prob)
                          (with-slots (i p c) prob
                            (/ (+ (* 100 i p) c)
                               (float p)))))))
    (print-line (solve problem-lst g 0))))

(defun solve (lst max-score num)
  (if (null lst)
      num
      (let ((comp (get-complete-score (car lst))))
        (if (> comp max-score)
            (solve-latter lst max-score num)
            (solve (cdr lst)
                   (- max-score comp)
                   (+ num (problem-p (car lst))))))))

(defun solve-latter (lst rem-score num)
  (+ num
     (min (loop for prob in lst
                minimize (with-slots (i p c) prob
                           (let ((p-needed (ceiling rem-score (* 100 i))))
                             (if (> p-needed p)
                                 most-positive-fixnum
                                 p-needed))))
          (loop for prob in lst
                minimize (if (>= (get-complete-score prob) rem-score)
                             (problem-p prob)
                             most-positive-fixnum)))))
#-swank(main)