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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

d, g = gets.chomp.split(' ').map(&:to_i)
list = d.times.map { gets.chomp.split(' ').map(&:to_i) }

board = list.map.with_index(1) do |line, k|
  cnt, bonus = line
  [0] + cnt.times.map do |i|
    j = i + 1
    if j == cnt
      j * 100 * k + bonus
    else
      j * 100 * k
    end
  end
end

def solve(ans, board, g, keys)
  new_ans = ans.map do |h|
    keys.map do |key|
      next if h[key] == board[key - 1].size - 1
      hd = h.dup
      hd[key] += 1
      hd
    end.compact
  end.flatten(1).uniq
  new_ans.each do |counts|
    total = counts.map { |i, cnt| board[i - 1][cnt] }.inject(:+)
    if total >= g
      return true
    end
  end
  new_ans
end

h = 1.upto(list.size).map { |i| [i, 0] }.to_h
ans = [h]

keys = h.keys
count = list.map(&:first).inject(:+)
1.upto(count).each do |i|
  ans = solve(ans, board, g, keys)
  if ans == true
    puts i
    break
  end
end