Problem:
Score : 400 points

Problem Statement

There are N one-off jobs available. If you take the i-th job and complete it, you will earn the reward of B_i after A_i days from the day you do it.

You can take and complete at most one of these jobs in a day.

However, you cannot retake a job that you have already done.

Find the maximum total reward that you can earn no later than M days from today.

You can already start working today.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i \leq 10^5

1 \leq B_i \leq 10^4

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 maximum total reward that you can earn no later than M days from today.

Sample Input 1

3 4
4 3
4 1
2 2

Sample Output 1

5

You can earn the total reward of 5 by taking the jobs as follows:

Take and complete the first job today. You will earn the reward of 3 after four days from today.

Take and complete the third job tomorrow. You will earn the reward of 2 after two days from tomorrow, that is, after three days from today.

Sample Input 2

5 3
1 2
1 3
1 4
2 1
2 3

Sample Output 2

10

Sample Input 3

1 1
2 1

Sample Output 3

0

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

--{-# LANGUAGE OverloadedStrings #-}
--{-# LANGUAGE OverloadedLists   #-}
{-# LANGUAGE BangPatterns      #-} --引数に!
{-# LANGUAGE MultiWayIf        #-}
{-# LANGUAGE TupleSections     #-}

import Data.Bits
import Data.Foldable (foldlM,foldrM)
import Data.Maybe (fromJust)
import Data.List
import Data.Array.Unboxed
import Data.Array.MArray
import Data.Array.ST
import Control.Monad
import Control.Monad.State
import Control.Monad.ST
import qualified Data.ByteString.Lazy.Char8 as B

solve :: Int -> Int -> Int -> [(Int,Int)] -> Int
solve n m i [] = 0
solve n m i ((a,b):ls) = if i+a <= m then b+(solve n m (i+1) ls) else solve n m i ls

main :: IO ()
main = do
  [n,m] <- map read.words <$> getLine :: IO [Int]
  ls <- replicateM n $ do
    [a,b] <- map read. words <$> getLine :: IO [Int]
    return (a,b)

  print $ solve n m 0 (sortOn (\(a,b) -> (-b,-a)) ls)