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: Accepted)

import sys
import collections

input = sys.stdin.readline


def main():
    N, M = [int(x) for x in input().split()]
    LRD = [[int(x) for x in input().split()] for _ in range(M)]
    A = [[] for j in range(N + 1)]

    if M == 0:
        print("Yes")
        return

    slist = set()
    for l, r, d in LRD:
        A[l].append([r, d])
        A[r].append([l, -d])
        slist.add(l)
        slist.add(r)

    dmemo = [None] * (N + 1)

    f = False
    for i in list(slist):
        if dmemo[i] is not None:
            continue
        s = collections.deque()
        s.append(i)
        dmemo[i] = 0

        while s:
            c = s.pop()
            for r, d in A[c]:
                if dmemo[r] is not None:
                    if dmemo[r] - dmemo[c] != d:
                        f = True
                        break
                else:
                    dmemo[r] = dmemo[c] + d
                    s.append(r)
            if f:
                break
        if f:
            break

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


if __name__ == '__main__':
    main()