Problem:
Score : 400 points

Problem Statement

Kenkoooo is planning a trip in Republic of Snuke.
In this country, there are n cities and m trains running.
The cities are numbered 1 through n, and the i-th train connects City u_i and v_i bidirectionally.
Any city can be reached from any city by changing trains.

Two currencies are used in the country: yen and snuuk.
Any train fare can be paid by both yen and snuuk.
The fare of the i-th train is a_i yen if paid in yen, and b_i snuuk if paid in snuuk.

In a city with a money exchange office, you can change 1 yen into 1 snuuk.
However, when you do a money exchange, you have to change all your yen into snuuk.
That is, if Kenkoooo does a money exchange when he has X yen, he will then have X snuuk.
Currently, there is a money exchange office in every city, but the office in City i will shut down in i years and can never be used in and after that year.

Kenkoooo is planning to depart City s with 10^{15} yen in his pocket and head for City t, and change his yen into snuuk in some city while traveling.
It is acceptable to do the exchange in City s or City t.

Kenkoooo would like to have as much snuuk as possible when he reaches City t by making the optimal choices for the route to travel and the city to do the exchange.
For each i=0,...,n-1, find the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i years.
You can assume that the trip finishes within the year.

Constraints

2 \leq n \leq 10^5

1 \leq m \leq 10^5

1 \leq s,t \leq n

s \neq t

1 \leq u_i < v_i \leq n

1 \leq a_i,b_i \leq 10^9

If i\neq j, then u_i \neq u_j or v_i \neq v_j.

Any city can be reached from any city by changing trains.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n m s t
u_1 v_1 a_1 b_1
:
u_m v_m a_m b_m

Output

Print n lines.
In the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.

Sample Input 1

4 3 2 3
1 4 1 100
1 2 1 10
1 3 20 1

Sample Output 1

999999999999998
999999999999989
999999999999979
999999999999897

After 0 years, it is optimal to do the exchange in City 1.

After 1 years, it is optimal to do the exchange in City 2.

Note that City 1 can still be visited even after the exchange office is closed.
Also note that, if it was allowed to keep 1 yen when do the exchange in City 2 and change the remaining yen into snuuk, we could reach City 3 with 999999999999998 snuuk, but this is NOT allowed.

After 2 years, it is optimal to do the exchange in City 3.

After 3 years, it is optimal to do the exchange in City 4.
Note that the same train can be used multiple times.

Sample Input 2

8 12 3 8
2 8 685087149 857180777
6 7 298270585 209942236
2 4 346080035 234079976
2 5 131857300 22507157
4 8 30723332 173476334
2 6 480845267 448565596
1 4 181424400 548830121
4 5 57429995 195056405
7 8 160277628 479932440
1 6 475692952 203530153
3 5 336869679 160714712
2 7 389775999 199123879

Sample Output 2

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE FlexibleContexts, ScopedTypeVariables, BangPatterns, OverloadedStrings #-}
{-# OPTIONS_GHC -O2 #-}

import Data.Array.IArray
import Data.Array.Unboxed
import Data.Array.ST
import Data.Char
import Data.List
import Data.Int
import qualified Data.Set as S
import qualified Data.ByteString.Char8 as B
import Control.Monad
import Control.Monad.ST

inf :: Int64
inf = 1000000000000000

getInts :: IO [Int]
getInts = unfoldr (B.readInt . B.dropWhile isSpace) <$> B.getLine

dijkstra :: Array Int [(Int, Int)] -> Int -> [Int64]
dijkstra g source = runST $ do
    ds :: STUArray s Int Int64 <- newArray (1, n) maxBound
    writeArray ds source 0
    let
      step :: S.Set (Int64, Int) -> ST s ()
      step q =
          case S.minView q of
            Nothing -> return ()
            Just ((d, v), q) -> do
              let
                relax q (u, w) = do
                    d <- readArray ds u

                    if d' < d
                      then do
                        writeArray ds u d'
                        return $ S.insert (d', u) q
                      else return q
                  where
                    d' = d + (fromIntegral w)

              foldM relax q (g!v) >>= step

    step $ S.singleton (0, source)

    ds' :: UArray Int Int64 <- freeze ds
    return (elems ds')
  where
    n = snd $ bounds g

main :: IO ()
main = do
	[n, m, s, t] <- getInts
	es <- replicateM m getInts
	let gy = accumArray (flip (:)) [] (1, n) $ concatMap (\[u, v, y, s] -> [(u, (v, y)), (v, (u, y))]) es
	let gs = accumArray (flip (:)) [] (1, n) $ concatMap (\[u, v, y, s] -> [(u, (v, s)), (v, (u, s))]) es
	putStrLn $ unwords $ map show $ map (inf-) $ scanr1 min $ zipWith (+) (dijkstra gy s) (dijkstra gs t)