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)

# 自然数xを0以上の整数n個に分割する順列を生成
# divide(10, 1) = [[10]]
# divide(10, 2) = [[0, 10], [1, 9], ...]
# divide(10, 3) = [[0, 0, 10], [0, 1, 9], ...]

def divide(x, n)
  if n == 1
    [[x]]
  else
    ret = []
    for i in 0..x
      for j in divide(x - i, n - 1)
        ret.push([i] + j)
      end
    end
    return ret
  end
end

D, G = gets.split.map(&:to_i)
QS = D.times.map{gets.split.map(&:to_i)}

table = []
indexes = []
sum = 0

D.times do |i|
  row = []
  num, bonus = QS[i]
  sum += num
  num.times do |j|
    indexes.push(i)
    point = (i + 1) * 100 * (j + 1)
    point += bonus if j == num - 1
    row.push(point)
  end
  table.push(row)
end

(1..sum).each do |n|
  div = divide(n, D)
  div.each do |ix|
    ans = 0
    ix.each_with_index do |m, i|
      point = table[i][m - 1]
      if m.zero? # 該当カテゴリ回答なし
        next
      end
      if point.nil? # 問題数超過
        ans = nil
        break
      end

      ans += point

      if ans >= G
        puts n
        exit
      end
    end
  end
end