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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

from bisect import bisect_left
from copy import deepcopy
from operator import itemgetter

n, m = (int(x) for x in input().split())
LRD = [tuple(int(x) for x in input().split()) for _ in range(m)]
LRD.sort(key=itemgetter(0, 1))
INF = 10**18

while LRD:
    X = [INF] * n
    TBD = []  # To be determined
    X[LRD[0][0] - 1] = 0
    for l, r, d in LRD:
        l -= 1
        r -= 1
        if X[l] == X[r] == INF:
            TBD.append((l, r, d))
        elif X[l] != INF and X[r] == INF:
            X[r] = X[l] + d
        elif X[l] == INF and X[r] != INF:
            X[l] = X[r] - d
        else:
            if X[r] - X[l] != d:
                print("No")
                exit()
            else:
                continue
    LRD = deepcopy(TBD)
    LRD.sort(key=itemgetter(0, 1))
    X.sort()
    xmax = X[bisect_left(X, INF) - 1]
    xmin = X[0]
    if xmax - xmin >= 10**9:
        print("No")
        exit()

print("Yes")