Problem:
Score : 400 points

Problem Statement

There are N people standing on the x-axis.
Let the coordinate of Person i be x_i.
For every i, x_i is an integer between 0 and 10^9 (inclusive).
It is possible that more than one person is standing at the same coordinate.

You will given M pieces of information regarding the positions of these people.
The i-th piece of information has the form (L_i, R_i, D_i).
This means that Person R_i is to the right of Person L_i by D_i units of distance, that is, x_{R_i} - x_{L_i} = D_i holds.

It turns out that some of these M pieces of information may be incorrect.
Determine if there exists a set of values (x_1, x_2, ..., x_N) that is consistent with the given pieces of information.

Constraints

1 \leq N \leq 100 000

0 \leq M \leq 200 000

1 \leq L_i, R_i \leq N (1 \leq i \leq M)

0 \leq D_i \leq 10 000 (1 \leq i \leq M)

L_i \neq R_i (1 \leq i \leq M)

If i \neq j, then (L_i, R_i) \neq (L_j, R_j) and (L_i, R_i) \neq (R_j, L_j).

D_i are integers.

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 D_1
L_2 R_2 D_2
:
L_M R_M D_M

Output

If there exists a set of values (x_1, x_2, ..., x_N) that is consistent with all given pieces of information, print Yes; if it does not exist, print No.

Sample Input 1

3 3
1 2 1
2 3 1
1 3 2

Sample Output 1

Yes

Some possible sets of values (x_1, x_2, x_3) are (0, 1, 2) and (101, 102, 103).

Sample Input 2

3 3
1 2 1
2 3 1
1 3 5

Sample Output 2

No

If the first two pieces of information are correct, x_3 - x_1 = 2 holds, which is contradictory to the last piece of information.

Sample Input 3

4 3
2 1 1
2 3 5
3 4 2

Sample Output 3

Yes

Sample Input 4

10 3
8 7 100
7 9 100
9 8 100

Sample Output 4

No

Sample Input 5

100 0

Sample Output 5

Yes

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

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UnboxedTuples #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE MultiWayIf #-}

import Control.Monad
import Control.Monad.ST
import Control.Monad.State
import Control.Applicative
import Data.List
import Data.Array
import Data.Array.IO
import Data.Array.ST
import Data.Maybe
import Data.Bits
import Data.Ord
import Data.Ratio
import Data.Int
import Data.Char
import qualified Data.ByteString.Char8 as BS
import qualified Data.Set as Set
import Data.Tuple
import Data.Function
import Text.Printf
import Debug.Trace
import Numeric

modifyArray arr i f = readArray arr i >>= \x -> writeArray arr i (f x)

listToTuple2 [a,b] = (a,b)
listToTuple3 [a,b,c] = (a,b,c)
listToTuple4 [a,b,c,d] = (a,b,c,d)
listToTuple5 [a,b,c,d,e] = (a,b,c,d,e)

getWords = getLine >>= return . words

readIntBS = fst . fromJust . BS.readInt

for = flip map

main :: IO ()
main = do
  (n,m) <- listToTuple2 . map read . words <$> getLine :: IO (Int,Int)
  es <- replicateM m $ listToTuple3 . map readIntBS . BS.words <$> BS.getLine :: IO [(Int,Int,Int)]

  check <- newArray (1,n) False :: IO (IOUArray Int Bool)
  dist <- newArray (1,n) 0 :: IO (IOUArray Int Int)
  
  let graph = buildWeightedDirectedGraph (1,n) es

  a <- (forM [1..n] $ \i -> dfs graph i check dist)

  putStrLn $ if and a then "Yes" else "No"

  where
    dfs :: Array Node [(Node,Cost)] -> Int -> IOUArray Int Bool -> IOUArray Int Int -> IO Bool
    dfs graph cur check dist = do
      writeArray check cur True
      res <- forM (graph!cur) $ \(next,d) -> do
        isChecked <- readArray check next
        if (not isChecked) then do
          readArray dist cur >>= \x -> writeArray dist next (x+d)
          dfs graph next check dist
          else do
          readArray dist cur >>= \x -> readArray dist next >>= \y -> return $ y == x+d
      return $ if null res then True else and res
  


type Node = Int
type Cost = Int

buildWeightedDirectedGraph :: (Node,Node) -> [(Node,Node,Cost)] -> Array Node [(Node,Cost)]
buildWeightedDirectedGraph bound dat = runST $ do
  graph <- newArray bound [] :: ST s (STArray s Node [(Node,Cost)])
  forM_ dat $ \(s,e,c) -> do
    modifyArray graph s ((e,c):)
    modifyArray graph e ((s,-c):)
  freeze graph