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 (2.7.1) (judge verdict: Accepted)

d, g = gets.chomp.split.map(&:to_i)
ary = d.times.map do
  gets.chomp.split.map(&:to_i)
end

ary = ary.map.with_index do |(p, c), idx|
 [p, c, p * (idx + 1) * 100 + c]
end
# [1,1,1,0,0]

ans = {
  sum: Float::INFINITY,
  pend_d_s: [],
  cnt: Float::INFINITY
}

# 全て選ぶか否かで、処理が変わるのでその分岐のためのswitchを作って全探索する。
(2**d).times do |i|
  switches = i.to_s(2).rjust(d, "0")
  record = {
    sum: 0,
    pend_d_s: [],
    cnt: 0
  }
  switches.chars.each_with_index do |s, idx|
    case s
    when "0" # 全選び
      record[:sum] += ary[idx].last
      record[:cnt] += ary[idx].first
    when "1" # 部分選びなので、出揃ってから処理する
      record[:pend_d_s].push idx
    end
  end

  # 合計値より低かったら、全選びでない奴らを、sumがgを超えるまで足す
  if record[:sum] <= g
    pends = record[:pend_d_s].sort
    until record[:sum] >= g || pends.empty? do
      some_d = pends.pop
      some_d_info = ary[some_d]
      shortage = ((g - record[:sum]) / ((some_d + 1) * 100).to_f).ceil
      if shortage < some_d_info.first
        record[:cnt] += shortage
        record[:sum] += shortage * ((some_d + 1) * 100)
      else
        record[:cnt] += some_d_info.first - 1
        record[:sum] += (some_d_info.first - 1) * ((some_d + 1) * 100)
      end
    end
  end

  if record[:sum] >= g && ans[:cnt] >= record[:cnt]
    ans = record
  end
end

puts ans[:cnt]