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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

data class Problems(var size: Int, val bonus: Int, val score: Int, val totalScore: Int)

fun main(args : Array<String>) {
    val (D, G) = readLine()!!.split(" ").map { it.toInt() }
    val problemSizeAndBonusScoreAndSingleScoreAndTotal = emptyList<Problems>().toMutableList()
    // O(D) = O(10)
    for (i in 1..D) {
        val (p, c) = readLine()!!.split(" ").map { it.toInt() }
        val score = 100 * i
        val total = score * p + c
        problemSizeAndBonusScoreAndSingleScoreAndTotal.add(Problems(p, c, score, total))
    }

    var a = emptyList<Triple<Int, Int, Boolean>>().toMutableList()

    for (i in 0..(problemSizeAndBonusScoreAndSingleScoreAndTotal.size - 1)) {
        val elm = problemSizeAndBonusScoreAndSingleScoreAndTotal.get(i)
        a.add(Triple(i, elm.totalScore, true))
        a.add(Triple(i, elm.score, false))
    }

    val set = setOf<Int>().toMutableSet()
    var answer = 0
    var objective = G

    while (objective > 0) {

        // sort by current efficiency
        a.sortByDescending {
            if (it.third) {
                val origin = problemSizeAndBonusScoreAndSingleScoreAndTotal.get(it.first)
                if (origin.size == 0) {
                    Int.MIN_VALUE
                } else {
                    Math.min(objective, it.second) / origin.size
                }
            } else {
                it.second
            }
        }

        // get top
        // if that is bunch type,
        val top = a.first()

        if (set.contains(top.first)) {
        } else {
            val origin = problemSizeAndBonusScoreAndSingleScoreAndTotal.get(top.first)
            if (top.third) {
                if (objective <= origin.totalScore - origin.bonus) {
                    while (origin.size > 0 && objective > 0) {
                        objective -= origin.score
                        answer++
                        origin.size--
                    }
                } else {
                    objective -= origin.totalScore
                    answer += origin.size
                    origin.size = 0
                }
            } else {
                while (origin.size > 0 && objective > 0) {
                    objective -= origin.score
                    answer++
                    origin.size--
                }
            }

            set.add(top.first)
        }
        a = a.drop(1).toMutableList()
    }

    println(answer)
}