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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]

use std::collections::*;
use std::cmp::Ordering;

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let d: usize = iter.next().unwrap().parse().unwrap();
    let g: i64 = iter.next().unwrap().parse().unwrap();
    let mut p: Vec<i64> = Vec::with_capacity(d);
    let mut c: Vec<i64> = Vec::with_capacity(d);
    
    for _ in 0..d {
        p.push(iter.next().unwrap().parse().unwrap());
        c.push(iter.next().unwrap().parse().unwrap());
    }

    let mut best_eff: Vec<i64> = Vec::with_capacity(d);
    let mut complete: Vec<i64> = Vec::with_capacity(d);
    
    for i in 0..d {
        best_eff.push((i as i64 +1)*100*(p[i] - 1));
        complete.push((i as i64 +1)*100*p[i] + c[i]);
    }

    let mut hset = (0..d).collect::<HashSet<_>>();

    println!("{}", calc(d, g, &mut hset, &best_eff, &complete, &p));
}

fn calc(d: usize, rest_score: i64, problems: &mut HashSet<usize>, best_eff: &[i64], complete: &[i64], p: &[i64]) -> i64 {
    if rest_score <= 0 {
        return 0;
    }

    let mut min = 1i64 << 60;

    let mut max_best_eff = 0;
    let mut max_bset_eff_p = 0i64;
    for &prob in problems.iter() {
        if max_best_eff < best_eff[prob] {
            max_best_eff = best_eff[prob];
            max_bset_eff_p = prob as i64;
        }
    }
    if max_best_eff >= rest_score {
        min = std::cmp::min(min, 
            if rest_score % (100 * (max_bset_eff_p + 1)) == 0 {
                rest_score / (100 * (max_bset_eff_p + 1))
            } else {
                rest_score / (100 * (max_bset_eff_p + 1)) + 1
            }
        );
    }
    let problems_clone: Vec<_> = problems.iter().cloned().collect();
    for prob in problems_clone {
        problems.remove(&prob);
        min = std::cmp::min(
            min,
            p[prob] + calc(d,rest_score - complete[prob],problems,best_eff,complete,p)
        );
        problems.insert(prob);
    }
    min
}