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)

from collections import deque
class UnionFind:
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def roots(self):
        return {i for i, x in enumerate(self.parents) if x < 0}


n, m = map(int, input().split())
graph = []
uf = UnionFind(n+1)
for _ in range(m):
    l, r, d = map(int, input().split())
    uf.union(l, r)
    graph.append((l, r, d))

x = {}
ans = "Yes"
re_check = deque([])
# 根の座標を０で確定
for i, y in enumerate(uf.parents):
    if y < 0:
        x[i] = 0

for l, r, d in graph:
    if l in x.keys() and r in x.keys():
        if x[r] - x[l] != d:
            ans = "No"
            break
    elif l in x.keys():
        x[r] = x[l] + d
    elif r in x.keys():
        x[l] = x[r] - d
    else:
        re_check.append((l, r, d))

while re_check and ans == "Yes":
    l, r, d = re_check.popleft()
    if l in x.keys() and r in x.keys():
        if x[r] - x[l] != d:
            ans = "No"
        continue
    if l in x.keys():
        x[r] = x[l] + d
    elif r in x.keys():
        x[l] = x[r] - d
    else:
        re_check.append((l, r, d))

if max(x.values()) - min(x.values()) > 10**9:
    ans = "No"

print(ans)