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.split.map(&:to_i)
g/=100
p=Array.new(d+1)
c=Array.new(d+1)
d.times{|i|
  p[i+1],c[i+1]=gets.split.map(&:to_i)
  c[i+1]/=100
}
require 'pp'
dp=Array.new(d+500000).map{Array.new()}
dp[0] << [Marshal.load(Marshal.dump(p)),0]
0.upto(g-1){|i|
  for condi in dp[i] do
    for j in 1..d do
      if condi[0][j]!=p[j] then break end
      if condi[0][j]>0 then
        for k in 1..condi[0][j] do
          np=Marshal.load(Marshal.dump(condi[0]))
          if i+np[j]*j+c[j]<g then 
            k=np[j]
            np[j]=0
            
            dp[i+k*j+c[j]] << [np,condi[1]+k]
            break
          end
          np[j]-=k
          dp[i+k*j+(np[j]==0? c[j]:0)] << [np,condi[1]+k]
          if i+k*j>=g then break end
        end
      end
    end
  end
}
  minc=nil
for i in g..500000 do
  for condi in dp[i] do
    if minc==nil || condi[1]<minc then minc=condi[1]
    end
  end
end
p minc