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)

use std::io::stdin;
use std::iter::repeat;

fn read_ints() -> Vec<i32> {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace().map(|token| token.parse().unwrap()).collect()
}

fn main () {
    let params = read_ints();
    let d: i32 = *params.get(0).unwrap();
    let g: i32 = *params.get(1).unwrap();

    let problem_params: Vec<_> = (0..d).map(|_d| {
        let vec = read_ints();
        (*vec.get(0).unwrap(), *vec.get(1).unwrap())
    }).collect();

    let answer = (0..(1 as i32).rotate_left(d as u32))
        .map(|complete_bits| {
            let is_complete = |_d: &i32| {
                complete_bits.rotate_right(*_d as u32) & 1 == 1
            };
            let complete_params: Vec<_> = (0..d)
                .filter(&is_complete)
                .map(|_d| {
                    let (count, bonus) = *problem_params.get(_d as usize).unwrap();
                    (_d + 1, count, bonus)
                }).collect();
            let complete_scores = complete_params.iter().map(|&(difficulty, count, bonus)| {
                difficulty * count * 100 + bonus
            }).fold(0, |x, y| x + y);
            let complete_counts = complete_params.iter().map(|&(difficulty, count, bonus)| {
                count
            }).fold(0, |x, y| x + y);

            if complete_scores >= g {
                Some(complete_counts)
            } else {
                let incomplete_params: Vec<_> = (0..d)
                    .filter(|x| !&is_complete(x))
                    .map(|_d| {
                        let &(count, bonus) = problem_params.get(_d as usize).unwrap();
                        ((_d + 1) * 100, count)
                    }).collect();
                let mut incomplete_problems: Vec<_> = incomplete_params.into_iter().flat_map(|(score, count)| repeat(score).take(count as usize)).collect();
                incomplete_problems.sort_by_key(|&x| -x);

                let mut scores_to_goal = g - complete_scores;
                let mut incomplete_counts = 0;
                for score in incomplete_problems.into_iter() {
                    if scores_to_goal > 0 {
                        scores_to_goal -= score;
                        incomplete_counts += 1;
                    }
                }
                if scores_to_goal <= 0 {
                    Some(incomplete_counts + complete_counts)
                } else {
                    None
                }
            }
        })
        .flat_map(|res| res.into_iter())
        .min_by_key(|&x| x).unwrap();

    println!("{}", answer)
}