Problem:
Score : 300 points

Problem Statement

Hearing that energy drinks increase rating in those sites, Takahashi decides to buy up M cans of energy drinks.

There are N stores that sell energy drinks. In the i-th store, he can buy at most B_i cans of energy drinks for A_i yen (the currency of Japan) each.

What is the minimum amount of money with which he can buy M cans of energy drinks?

It is guaranteed that, in the given inputs, a sufficient amount of money can always buy M cans of energy drinks.

Constraints

All values in input are integers.

1 \leq N, M \leq 10^5

1 \leq A_i \leq 10^9

1 \leq B_i \leq 10^5

B_1 + ... + B_N \geq M

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
\vdots
A_N B_N

Output

Print the minimum amount of money with which Takahashi can buy M cans of energy drinks.

Sample Input 1

2 5
4 9
2 4

Sample Output 1

12

With 12 yen, we can buy one drink at the first store and four drinks at the second store, for the total of five drinks. However, we cannot buy 5 drinks with 11 yen or less.

Sample Input 2

4 30
6 18
2 5
3 10
7 9

Sample Output 2

130

Sample Input 3

1 100000
1000000000 100000

Sample Output 3

100000000000000

The output may not fit into a 32-bit integer type.

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

{-# LANGUAGE BangPatterns #-}
import Data.Int
import Data.List hiding (insert)
import qualified Data.ByteString.Char8 as BS

data Tree = Empty
          | Bin {- key (yen) -} {-# UNPACK #-} !Int64
                {- value (number of drink) -} {-# UNPACK #-} !Int
                {- total cost (yen) -} {-# UNPACK #-} !Int64
                {- total number of drink -} {-# UNPACK #-} !Int
                Tree Tree

insert :: Int64 -> Int -> Tree -> Tree
insert !k !v Empty = Bin k v (k * fromIntegral v) v Empty Empty
insert !k !v (Bin k' v' tc tn s t) = case compare k k' of
  LT -> Bin k' v' tc' tn' (insert k v s) t
  EQ -> Bin k (v + v') tc' tn' s t
  GT -> Bin k' v' tc' tn' s (insert k v t)
  where tc' = tc + k * fromIntegral v
        tn' = tn + v

toList :: Tree -> [(Int64,Int)]
toList = go []
  where
    go xs Empty = xs
    go xs (Bin k v _ _ s t) = go ((k,v) : go xs t) s

total :: Tree -> (Int64,Int)
total Empty = (0,0)
total (Bin _ _ tc tn _ _) = (tc,tn)

main = do
  [n,m] <- map (read . BS.unpack) . BS.words <$> BS.getLine
  ab <- fmap (foldl' (flip $ uncurry insert) Empty) $ sequence $ replicate n $ do
    [a,b] <- map (read . BS.unpack) . BS.words <$> BS.getLine
    return (a :: Int64, fromIntegral b :: Int) -- (a :: Int64, b :: Int)
  let solve !k !yen (Bin a b _ _ s t) | k < ln = solve k yen s
                                      | k <= ln + b = yen + lc + a * fromIntegral (k - ln)
                                      | otherwise = solve (k - ln - b) (yen + lc) t
        where (lc,ln) = total s
  print $ solve m 0 ab