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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    static int ans = Integer.MAX_VALUE;
    static int max = 0;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int goalScore = sc.nextInt();
        int[] points = new int[n];
        HashMap<Integer, Integer> map = new HashMap<>();
        int[] bonusPoints = new int[n];
        for (int i = 0; i < n; i++) {
            map.put((i + 1) * 100, sc.nextInt());
            bonusPoints[i] = sc.nextInt();
        }
        int num = 0;
        int currentScore = 0;
        int maxPoint = n * 100;
        max = maxPoint;
        hoge: for(int i = 0; i < map.size(); i++) {
            int numOfQuestions = map.get(maxPoint);
            while(numOfQuestions > 0) {
                num++;
                currentScore += maxPoint;
                if(numOfQuestions == 1) currentScore += bonusPoints[n-1];
                if(currentScore >= goalScore) {
                    ans = Math.min(ans, num);
                    break hoge;
                }
                numOfQuestions--;
            }
            maxPoint -= 100;
        }
        solve(0, goalScore, 0, map, maxPoint, bonusPoints);
        System.out.println(ans);
    }
    private static void solve(int currentScore, int goalScore, int numOfQuestions, HashMap<Integer, Integer> map, int pointKey, int[] bonus) {
        if(currentScore >= goalScore) {
            ans = Math.min(ans, numOfQuestions);
            return;
        }
        int maxPoint = max;
        while(maxPoint > 0) {
            int remainQuesions = map.get(maxPoint);
            if(remainQuesions != 0) {
                for(int i = 0; i < remainQuesions; i++) {
                    numOfQuestions++;
                    currentScore += maxPoint;
                    if(currentScore >= goalScore) {
                        ans = Math.min(ans, numOfQuestions);
                        return;
                    }
                }
            }
            maxPoint -= 100;
        }
        if(pointKey <= 0) return;
        int num = map.get(pointKey);
        map.put(pointKey, 0);
        solve(currentScore + (pointKey * num + bonus[pointKey / 100 - 1]), goalScore, numOfQuestions + num, map, pointKey - 100, bonus);
        map.put(pointKey, num);
        solve(currentScore, goalScore, numOfQuestions, map, pointKey - 100, bonus);
    }
}