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: Accepted)

{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE BangPatterns #-}

import qualified Data.ByteString.Char8 as B
import Data.Attoparsec.ByteString.Char8
import Data.List (sort)

type Input  = (Int, Int, [(Int, Int)])
type Output = Int

input :: Parser Input
input = do
  (_N, _M) <- decimalPair
  _ABs <- count _N decimalPair
  return (_N, _M, _ABs)

decimalPair :: Parser (Int, Int)
decimalPair = (,)
  <$> decimal <* char ' '
  <*> decimal <* endOfLine

main :: IO ()
main = B.interact
  $ B.pack . show . either (error "parse err") solve . parseOnly input

solve :: Input -> Output
solve (_N, _M, _ABs) = go 0 _M $ sort _ABs
  where
    go !n !m ((a, b) : abs)
      | m <= b    = n + a * m
      | otherwise = go (n + a * b) (m - b) abs