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: Accepted)

import java.util.*;

public class Main {
	static Test[] tests;
	static int d;
	static int g;

	public static void main (String[] args)  {
		Scanner sc = new Scanner(System.in);
		d = sc.nextInt();
		g = sc.nextInt();
		tests = new Test[d];
		for (int i = 0; i < d; i++) {
			int a = sc.nextInt();
			int b = sc.nextInt();
			tests[i] = new Test(i + 1, a, b);
		}
		System.out.println(getResult(0, 0, 0, 0, 0).count);
	}
	
	static Result getResult(int idx, int count, int point, int rCount, int rPoint) {
		if (point >= g) {
			return new Result(count, point);
		}
		if (idx >= d) {
			for (int i = 1; i <= rCount; i++) {
				if (point + i * rPoint >= g) {
					return new Result(count + i, g);
				}
			}
			return null;
		}
		Result r1 = getResult(idx + 1, count + tests[idx].count, point + tests[idx].getBonus(), rCount, rPoint);
		Result r2 = getResult(idx + 1, count, point, tests[idx].count - 1, tests[idx].getPoint());
		if (r1 == null) {
			return r2;
		} else if (r2 == null) {
			return r1;
		} else {
			if (r2.count < r1.count) {
				return r2;
			} else {
				return r1;
			}
		}
	}
	
	static class Result {
		int count;
		int point;
		
		public Result(int count, int point) {
			this.count = count;
			this.point = point;
		}
		
		public String toString() {
			return "count:" + count + " point:" + point;
		}
	}
	
	static class Test {
		int idx;
		int count;
		int bonus;
		
		public Test(int idx, int count, int bonus) {
			this.idx = idx;
			this.count = count;
			this.bonus = bonus;
		}
		
		public int getBonus() {
			return count * getPoint() + bonus;
		}
		
		public int getPoint() {
			return idx * 100;
		}
	}
}