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)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	sc.Scan()
	D, _ := strconv.Atoi(sc.Text())

	sc.Scan()
	G, _ := strconv.Atoi(sc.Text())

	problems := make([][]int, D)
	for i := 0; i < D; i++ {
		sc.Scan()
		p, _ := strconv.Atoi(sc.Text())

		sc.Scan()
		c, _ := strconv.Atoi(sc.Text())

		problems[i] = []int{p, c}
	}

	minCount := math.MaxInt64
	for i := 0; i < 2<<uint(D); i++ {
		count := 0
		score := 0
		maxZeroIndex := -1
		for j := 0; j < D; j++ {
			if i>>uint(j)&1 == 1 {
				problem := problems[j]
				count += problem[0]
				score += problem[1] + problem[0]*(j+1)*100
			} else {
				maxZeroIndex = j
			}
		}

		if score >= G {
			if count < minCount {
				minCount = count
			}
		} else if maxZeroIndex != -1 {
			restCount := (G - score) / ((maxZeroIndex + 1) * 100)
			if (G-score)%((maxZeroIndex+1)*100) != 0 {
				restCount++
			}
			if restCount <= problems[maxZeroIndex][0] {
				count += restCount
				if count < minCount {
					minCount = count
				}
			}
		}
	}
	fmt.Println(minCount)
}

func min(s ...int) int {
	minContent := s[0]
	for _, el := range s {
		if el < minContent {
			minContent = el
		}
	}
	return minContent
}