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: Wrong Answer)

# 人を頂点と見なしたグラフを作る。有向で、逆向きの場合は正負を反転させて辺を張る
# 頂点からの距離を記録し、一致しない箇所があればNG。
# 全ての辺を通るまで続ける。
# 辺の情報を[{0から行ける頂点},{1から行ける頂点},...]で管理する
# 親には進まないようにしてDFSする

N,M = map(int,input().split())
E = [[] for i in range(N)]
for i in range(M):
  L,R,D = map(int,input().split())
  E[L-1].append([R-1,D])
  E[R-1].append([L-1,-D])
from collections import deque
# 頂点、親、距離
dist = [-1] * N
for i in range(N):
  if dist[i] != -1:
    continue
  dist[i] = 0
  q = deque()
  q.append([i,-1])
  while q:
    v,parent = q.pop()
    for child in E[v]:
      if child[0] == parent:
        continue
      if dist[child[0]] == -1:
        dist[child[0]] = dist[v] + child[1]
        q.append([child[0],v])
      else:
        if dist[child[0]] != dist[v] + child[1]:
          print("No")
          exit(0)
else:
  print("Yes")