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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE TupleSections #-}
import Data.List
import qualified Data.ByteString.Char8 as B
import Control.Monad.State (State, evalState, gets, modify)
import Data.Map.Strict (Map, lookup, insert, empty)
import Data.Maybe (maybe)
import Control.Monad
main :: IO ()
main = breads >>= main'
    where
        main' [d, g] = replicateM d breads >>= print . solve g

-- |
-- >>> solve 700 [[3,500],[5,800]]
-- 3
--
-- >>> solve 2000 [[3,500],[5,800]]
-- 7
--
-- >>> solve 400 [[3,500],[5,800]]
-- 2
--
-- >>> solve 25000 [[20,1000],[40,1000],[50,1000],[30,1000],[1,1000]]
-- 66
solve :: Int -> [[Int]] -> Int
solve g pcs = run calc . (g, [],) . map build $ zip pcs [1..]
    where
        build ([p, c], i) = (100 * p * i + c, p, 100 * i)

        calc f (r, ps, (w, c, p) : xs)
            | r > 0 = minimum <$> sequence [(+ c) <$> f (r - w, ps, xs), f (r, (c - 1, p) : ps, xs)]
            | otherwise = return 0
        calc _ (r, ps, _)
            | r > 0 = return . calc2 r . sortBy cmpf $ filter (\(c, _) -> c > 0) ps
            | otherwise = return 0
            where
                cmpf (_, lp) (_, rp) = compare rp lp
        
        calc2 r ((c, p) : xs)
            | r >= cp = c + calc2 (r - cp) xs
            | r > 0 = v
            | otherwise = 0
            where
                cp = c * p
                (a, m) = r `divMod` p
                v
                    | m > 0 = a + 1
                    | otherwise = a
        calc2 r _
            | r > 0 = 100000
            | otherwise = 0


type Memoizer a b = a -> State (Map a b) b

run :: (Ord a) => (Memoizer a b -> Memoizer a b) -> a -> b
run f = flip evalState empty . memoizeFix f

memoizeFix :: (Ord a) => (Memoizer a b -> Memoizer a b) -> Memoizer a b
memoizeFix f x = gets (Data.Map.Strict.lookup x) >>= maybe (f (memoizeFix f) x >>= ((<$) <*> (modify . Data.Map.Strict.insert x))) return

breads :: IO [Int]
breads = unfoldr uff <$> B.getLine
    where
        uff b = check <$> B.readInt b
        check (a, b)
            | B.null b = (a, b)
            | otherwise = (a, B.tail b)