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)

from collections import defaultdict

N_PEOPLE, N_INFO = list(map(int, input().split()))

info_list = []
for i in range(N_INFO):
  l, r, d = list(map(int, input().split()))
  info_list.append({
    "left":  l-1,
    "right": r-1,
    "dist":  d
  })

# 与えられた条件を満たす場合があるか
fulfill_conditions = True

# 各人の位置(不定の場合は-1)
locations = [-1] * N_PEOPLE

# 各人が登場したか
appeared = []

# 各人の関係グラフ
relation = defaultdict(lambda: [])

for info in info_list:
  # 左右の人物が共に初登場なら，とりあえずleftを0において，rightを距離の分だけ離す
  if info["left"] not in appeared and info["right"] not in appeared:
    locations[info["left"]] = 0
    locations[info["right"]] = info["dist"]

    appeared.append(info["left"])
    appeared.append(info["right"])

    relation[info["left"]].append(info["right"])
    relation[info["right"]].append(info["left"])

    continue

  # 左の人物だけが初登場なら，rightの人物の位置から見てdist分左におく
  if info["left"] not in appeared and info["right"] in appeared:
    locations[info["left"]] = locations[info["right"]] - info["dist"]

    # 左に置くと範囲外になるなら，それを0に設置して，
    # 超過した分だけ他の人を右にずらす
    if locations[info["left"]] < 0:
      exceeded_dist = -1 * locations[info["left"]]
      locations[info["left"]] = 0

      for index in relation[info["right"]]:
        locations[index] += exceeded_dist

      if max(locations) > 10**9:
        fulfill_conditions = False
        break

    appeared.append(info["left"])
    relation[info["left"]].append(info["right"])
    relation[info["right"]].append(info["left"])

    continue


  # 右の人物だけが初登場なら，leftの人物から見てdist分右におく
  if info["left"] in appeared and info["right"] not in appeared:
    locations[info["right"]] = locations[info["left"]] + info["dist"]

    # 右に置くと範囲外になるなら，それを10**9に設置して，
    # 超過した分だけ他の人を左にずらす
    if locations[info["right"]] > 10**9:
      exceeded_dist = locations[info["right"]] - (10**9)
      locations[info["right"]] = 10**9

      for index in relation[info["left"]]:
        locations[index] += exceeded_dist

      if min(locations) < 0:
        fulfill_conditions = False
        break

    appeared.append(info["right"])
    relation[info["left"]].append(info["right"])
    relation[info["right"]].append(info["left"])

    continue

  # 両方の人物が既出なら，距離が正しいかチェックする
  # 正しくなければアウト
  if info["left"] in appeared and info["right"] in appeared:
    if locations[info["right"]] - locations[info["left"]] != info["dist"]:

      fulfill_conditions = False
      break

    relation[info["left"]].append(info["right"])
    relation[info["right"]].append(info["left"])

if fulfill_conditions:
  print("Yes")
else:
  print("No")