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: Time Limit Exceeded)

import Control.Applicative
import Control.Monad
import qualified Data.IntSet as IS
import qualified Data.IntMap as IM

data Spectrum = Spectrum (IM.IntMap Int) | Info Int

main :: IO()
main = do
    [n,m] <- map read . words <$> getLine
    lrds <- replicateM m $ map read . words <$> getLine
    putStrLn $ isCons (IM.fromSet (\k -> Spectrum (IM.singleton k 0)) (IS.fromList [1..n])) lrds
        where
            isCons :: IM.IntMap Spectrum -> [[Int]] -> String
            isCons _ [] = "Yes"
            isCons m ([l,r,d]:lrds)
                | or (IM.intersectionWith (/=) lm' rm') = "No"
                | otherwise = isCons (IM.insert ri (Info li) $ IM.insert li (Spectrum (IM.union lm' rm')) m) lrds
                where
                    (li,lm,lx) = find m l l
                    (ri,rm,rx) = find m r r
                    lm' = fmap (+rx) lm
                    rm' = fmap (+(lx+d)) rm
                    find m a i =
                        case m IM.! a of
                            Spectrum am -> (a, am, am IM.! i)
                            Info a' -> find m a' i