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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import sys
sys.setrecursionlimit(10**6)

def get_par(x):
  if x == par_list[x]:
    return x
  else:
    par_list[x] = get_par(par_list[x])
    return par_list[x]

def merge(x,y):
  par_x = get_par(x)
  par_y = get_par(y)
  if par_x != par_y:
    par_list[par_y] = par_x

def is_same(x,y):
  return get_par(x) == get_par(y)

N,M=map(int,input().split())
par_list = list(range(N+1))

lrdlist=[]
for i in range(M):
  L,R,D=map(int,input().split())
  if L<R:
    lrdlist.append((L,R,D))
    merge(L,R)
  else:
    lrdlist.append((R,L,-D))  
    merge(R,L)
lrdlist.sort()
#print(lrdlist)
for i in range(1,N+1):
  par_list[i]=get_par(i)
#print(par_list)

array=[0]+[-10**9]*(N)
for i in range(1,N+1):
  if par_list[i]==i:
    array[i]=0
#print(array)

lrdlist2=[]
while(len(lrdlist)>0):
  lrdlist2=[]
  for L,R,D in lrdlist:
    if array[L]==-10**9:
      if array[R]==-10**9:
        lrdlist2.append((L,R,D))
      else:
        array[L]=array[R]-D
    else:
      if array[R]==-10**9:
        array[R]=array[L]+D
      else:
        if array[R]!=array[L]+D:
          print("No")
          sys.exit(0)
  lrdlist=lrdlist2

#print(array[1:])
print("Yes")