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 OCaml (4.02.3) (judge verdict: Accepted)

(* O(2^d d) *)
Scanf.scanf " %d %d" @@ fun d g ->
  let pcs = Array.init d @@ fun _ -> Scanf.scanf " %d %d" @@ fun p c -> p, c in
  let ans = ref max_int in
  let rec find acc rest i bits =
    if rest <= 0 then acc
    else if i < 0 then max_int
    else if bits lsr i land 1 = 1 then find acc rest (i - 1) bits
    else
      let p, _ = pcs.(i) in
      let m = (i + 1) * 100 in
      let n = min (p - 1) @@ (rest + m - 1) / m in
      find (acc + n) (rest - n * m) (i - 1) bits in
  let points = Array.init d @@ fun i -> let p, c = pcs.(i) in i, p, p * (i + 1) * 100 + c in
  let f bits =
    let g (c, sum) (i, p, s) = if bits lsr i land 1 = 1 then c + p, sum + s else c, sum in
    Array.fold_left g (0, 0) points in
  for i = 0 to 1 lsl d - 1 do
    let c, s = f i in
    ans := min !ans @@ find c (g - s) (d - 1) i
  done;
  Printf.printf "%d\n" !ans