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)

import java.io.*
import java.util.*

fun solve(D: Int, G: Int, p: IntArray, c: IntArray){
    // 中途半端に解くのは一種類以下で、完答してない中で一番高い点数のもの
    // 完答リスト
    val combs = (0 until D).toSet().powerSet()
    val candidates = mutableListOf<Int>()
    for (comb in combs){
        val point = comb.map{ p[it] * (it+1)* 100 + c[it] }.sum()
        val quant = comb.map{ p[it] }.sum()
        if (point >= G) candidates.add(quant)
        else{
            val m = (0 until D).toList().filter{ it !in comb }.max()?: continue
            val ret = (G - point) / (100*(m+1)) + if((G-point) % 100*(m+1) == 0 ) 0 else 1
            if (ret <= p[m] && point + ret * (m+1)*100 >= G) candidates.add(quant + ret)
        }
    }
    println(candidates.min())
    return
}

fun <T> Collection<T>.powerSet(): Set<Set<T>> = powerSet(this, setOf(setOf()))

private tailrec fun <T> powerSet(left: Collection<T>, acc: Set<Set<T>>): Set<Set<T>> = when {
    left.isEmpty() -> acc
    else ->powerSet(left.drop(1), acc + acc.map { it + left.first() })
}

fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }
    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }
    val sc = Scanner(System.`in`)
    val D = sc.next().toInt()
    val G = sc.next().toInt()
    val p = IntArray(D)
    val c = IntArray(D)
    for (i in 0 until D) {
        p[i] = sc.next().toInt()
        c[i] = sc.next().toInt()
    }
    solve(D, G, p, c)
}