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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Diagnostics;

namespace P_AtCoder
{
    class Program
    {
        class ScoreItem
        {
            public int Level { get; set; }
            public int Count { get; set; }
            public int CompleteBouns { get; set; }
        }

        static int _maxLevel { get; set; }
        static int _goal { get; set; }

        static List<ScoreItem> QuestionList { get; set; }
        static int? result;

        static void Main(string[] args)
        {
            var cache = Console.ReadLine().Split(' ');
            _maxLevel = int.Parse(cache[0]);
            _goal = int.Parse(cache[1]);

            QuestionList = new List<ScoreItem>();
            for (int lv = 1; lv <= _maxLevel; lv++)
            {
                var addCache = new ScoreItem() { Level = lv };
                var inputStr = Console.ReadLine().Split(' ');
                addCache.Count = int.Parse(inputStr[0]);
                addCache.CompleteBouns = int.Parse(inputStr[1]);
                QuestionList.Add(addCache);
            }

            result = null;
            //Recursion
            CalcRecursion(1, 0, 0, false);

            Console.WriteLine(result);
        }

        static void CalcRecursion(int nowLevel, int beforeAns, int beforeScore, bool useIncomplete)
        {
            if (beforeScore >= _goal)
            {
                if (!result.HasValue)
                {
                    result = beforeAns;
                    return;
                }
                else if (beforeAns < result.Value)
                {
                    result = beforeAns;
                    return;
                }
            }

            var nowSet = QuestionList.FirstOrDefault(x => x.Level == nowLevel);
            if (nowSet == null)
            {
                return;
            }

            CalcRecursion(
                nowLevel + 1,
                beforeAns + nowSet.Count,
                beforeScore + (nowSet.Level * nowSet.Count * 100) + nowSet.CompleteBouns,
                useIncomplete);

            CalcRecursion(
                nowLevel + 1,
                beforeAns,
                beforeScore,
                useIncomplete);

            if (!useIncomplete)
            {
                for (int ct = 1; ct < nowSet.Count; ct++)
                {
                    CalcRecursion(nowLevel + 1, beforeAns + ct, beforeScore + (ct * nowSet.Level * 100), true);
                }
            }
        }
    }
}