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
  ScopedTypeVariables, BangPatterns, TupleSections, ExplicitForAll,
  LambdaCase, MultiWayIf, Unsafe, RecordWildCards, FlexibleContexts, CPP,
  NoMonomorphismRestriction, GADTs,
  RankNTypes, EmptyDataDecls, EmptyCase, ViewPatterns #-}


import Data.Bits
import Data.List
import Data.Maybe
import Data.Tuple
import Data.Ord
import Data.Int
import Data.Word
import Data.Char
import Data.Function
import Data.STRef
import Data.IORef
import Data.Monoid
import Data.Functor
import System.IO
import Control.Applicative
import Control.Monad
import Control.Monad.Primitive
import Control.Monad.State.Strict
import Control.Monad.ST
import Control.Monad.ST.Lazy (strictToLazyST, lazyToStrictST)
import qualified Control.Monad.ST.Lazy as STL
-- import Control.Monad.ST.Safe
import Control.DeepSeq
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy.Char8 as BSL
import qualified Data.ByteString.Builder as BSB
import Data.IntMap (IntMap)
import qualified Data.IntMap.Strict as IMS
import qualified Data.IntMap.Lazy as IML
import Data.IntSet (IntSet)
import qualified Data.IntSet as IS
import qualified Data.Sequence as Seq
import Data.Sequence (Seq)
import qualified Data.Array.IArray as A
import qualified Data.Array.MArray.Safe as A
import qualified Data.Array.MArray as A
import Data.Array (Array)
import Data.Array.Unboxed (UArray)
import Data.Array.IArray (IArray)
import Data.Array.MArray.Safe (MArray)
import Data.Array.IO.Safe (IOArray, IOUArray)
import Data.Array.ST.Safe (STArray, STUArray, runSTArray, runSTUArray)
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector.Primitive as VP
import qualified Data.Vector.Primitive.Mutable as VPM
import qualified Data.Vector.Generic as VG
import qualified Data.Vector.Generic.Mutable as VGM

main :: IO ()
main = do
  [n,m] <- map readInt . words <$> getLine
  input <- sort . take n . 
  	unfoldr (runStateT $ (,) <$> rInt <*> rInt) <$> BSL.getContents
  print
   $ foldr (\(!v,!cnt) cont (!tot, !m) ->
                if cnt >= m then tot + m * v else cont (tot + cnt * v, m - cnt))
           (\(!tot, !m) -> undefined) input (0,m)

rInt :: StateT BSL.ByteString Maybe Int
rInt = StateT $ BSL.readInt . BSL.dropWhile (<'!')
rIntS :: StateT BS.ByteString Maybe Int
rIntS = StateT $ BS.readInt . BS.dropWhile (<'!')

#define D(f,r,d) f::Integral a=>a->d;f=fromIntegral;r::String->d;r=read
#define C(f,r,g,h,d) D(f,r,d);g,h::RealFrac a=>a->d;g=floor;h=ceiling
C(_toInteger_,readInteger,floorInteger,ceilInteger,Integer)
C(toInt,readInt,floorInt,ceilInt,Int)
C(toI8,readI8,floorI8,ceilI8,Int8)
C(toI16,readI16,floorI16,ceilI16,Int16)
C(toI32,readI32,floorI32,ceilI32,Int32)
C(toI64,readI64,floorI64,ceilI64,Int64)
C(toWord,readWord,floorWord,ceilWord,Word)
C(toW8,readW8,floorW8,ceilW8,Word8)
C(toW16,readW16,floorW16,ceilW16,Word16)
C(toW32,readW32,floorW32,ceilW32,Word32)
C(toW64,readW64,floorW64,ceilW64,Word64)
D(toDouble,readDouble,Double)
D(toFloat,readFloat,Float)
#undef D
#undef C

{-# INLINE wrA #-}
wrA = A.writeArray
{-# INLINE rdA #-}
rdA = A.readArray
{-# INLINE mdA #-}
mdA arr f i = do
  ai <- rdA arr i
  let fai = f ai 
  wrA arr i fai
  return (ai,fai)
{-# INLINE mdA' #-}
mdA' arr f i = do
  !ai <- rdA arr i
  let !fai = f ai
  wrA arr i fai
  return (ai,fai)
{-# INLINE swapA #-}
swapA arr i j = do
  ai <- rdA arr i
  wrA arr i =<< rdA arr j
  wrA arr j ai

#define N(f,g,a,m)\
  f :: forall e i s. (C(a,m)A.Ix i) => (i,i) -> e -> m (a i e); f=A.newArray;\
  g :: forall e i s. (C(a,m)A.Ix i) => (i,i) -> m (a i e); g=A.newArray_
#define C(a,m)
N(newIOA,newIOA_,IOArray,IO)
N(newSTA,newSTA_,STArray s,ST s)
#undef C
#define C(a,m) MArray (a) e (m), 
N(newIOUA,newIOUA_,IOUArray,IO)
N(newSTUA,newSTUA_,STUArray s,ST s)
#undef C
#undef N