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: Wrong Answer)

import qualified Data.ByteString.Lazy.Char8 as B
import Data.Maybe
import qualified Data.Vector.Unboxed.Mutable as VM
import Control.Monad
import Control.Monad.ST
import Debug.Trace

traceQ :: (Show a) => String -> a -> a
-- traceQ label a = trace (label ++ ": " ++ show a) a
traceQ _ a = a

traceZ :: String -> a -> a
-- traceZ = trace
traceZ _ a = a

bsReadInts :: B.ByteString -> [Int]
bsReadInts = map (fst . fromJust . B.readInt) . B.words

solve :: Int -> Int -> [[Int]] -> Bool
solve valN valM lrds = runST (act valN valM lrds)

act :: Int -> Int -> [[Int]] -> ST s Bool
act valN valM lrds = do
  vec <- VM.replicate (valN+1) (-1,-1)
  act1 lrds vec

act1 :: [[Int]] -> VM.MVector s (Int, Int) -> ST s Bool
act1 [] _ = return True
act1 ([l,r,d]:lrds) vec = do
  b <- step l r d vec
  if b
    then act1 lrds vec
    else return False

step :: Int -> Int -> Int -> VM.MVector s (Int, Int) -> ST s Bool
step l r d vec = do
  (prevL, distL) <- VM.read vec l
  (prevR, distR) <- VM.read vec r
  if distR == -1
    then do
    when (distL == -1) (VM.write vec l (-1, 0))
    VM.write vec (traceZ (show "A " ++ show r ++ "," ++ show l ++ "," ++ show d) r) (l, d)
    return True
    else
    if distL == -1
    then do
      VM.write vec (traceZ (show "B " ++ show l ++ "," ++ show r ++ "," ++ show (-d)) l) (r, -d)
      -- VM.write vec l (r, -d)
      return True
    else do
      (lTop, lTopDist) <- findTop vec l 
      (rTop, rTopDist) <- findTop vec r
      if lTop == rTop
        then
        if lTopDist + d == rTopDist
        then
          return True
        else
          return False
        else do
        VM.write vec rTop (lTop, lTopDist + d - rTopDist)
        return True

findTop :: VM.MVector s (Int, Int) -> Int -> ST s (Int, Int)
findTop vec x = ftsub 0 vec x
  where
    ftsub acc vec x = do
      (prev, dist) <- VM.read vec x
      if prev == -1 then return (x, acc)
        else ftsub (acc + dist) vec prev
        

main :: IO ()
main = do
  conts <- B.getContents
  let [valN, valM] : lrds = map bsReadInts (B.lines conts)
      answer = solve valN valM lrds
  putStrLn (if answer then "Yes" else "No")