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: Time Limit Exceeded)

module Main where

import qualified Data.Vector                   as V
import           Data.List
import           Control.Applicative
import           Control.Monad


main :: IO ()
main = do
  [n, m] <- map read . words <$> getLine
  ns     <-
    fmap (sortBy (\(a : _) (b : _) -> compare a b))
    .   replicateM n
    $   map read
    .   words
    <$> getLine

  let hmany =
        n - length (filter (\i -> sum i >= m) $ inits $ map (!! 1) ns) + 1

  print $ f1 (take hmany ns) 0 0 m

f1 []       _   mny _ = mny
f1 [n     ] cnt mny m = mny + (m - cnt) * head n
f1 (n : ns) cnt mny m = f1 ns (cnt + last n) (mny + last n * head n) m