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 Go (1.6) (judge verdict: Accepted)

// ProblemURL : https://atcoder.jp/contests/abc104/tasks/abc104_c
// ---------------------------------------------
package main

import "fmt"

var inf = 1 << 60

func smaller(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func main() {
	var n, targetScore int
	fmt.Scan(&n, &targetScore)
	type problem struct {
		point int
		count int
		bonus int
	}
	problems := make([]problem, n)
	for i := 0; i < n; i++ {
		var p, c int
		fmt.Scan(&p, &c)
		problems[i] = problem{
			point: (i + 1) * 100,
			count: p,
			bonus: c,
		}
	}
	ctSolvedMin := inf
	for i := 0; i < (1 << uint(n)); i++ {
		ctSolved := 0
		score := 0
		for j := 0; j < n; j++ {
			if i>>uint(j)&1 == 1 {
				ctSolved += problems[j].count
				score += problems[j].point * problems[j].count
				score += problems[j].bonus
			}
		}
		if score >= targetScore {
			ctSolvedMin = smaller(ctSolvedMin, ctSolved)
		} else {
			for j := n - 1; j >= 0; j-- {
				if i>>uint(j)&1 == 1 {
					continue
				}
				for h := 0; h < problems[j].count; h++ {
					ctSolved++
					score += problems[j].point
					if score >= targetScore {
						break
					}
				}
				if score >= targetScore {
					break
				}
			}
			ctSolvedMin = smaller(ctSolvedMin, ctSolved)
		}
	}
	fmt.Println(ctSolvedMin)
}