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
sys.setrecursionlimit(200002)

def try_dfs_fill_distance(graph, cur_node, cur_dist_from_origin, distance_cache):
    found_conflicts = False
    for neighbor_node_data in graph[cur_node]:
        neighbor_node, neighbor_distance_from_cur = neighbor_node_data
        neighbor_dist_from_origin = (cur_dist_from_origin + neighbor_distance_from_cur)
        #print("cur_node:{} neighbor_node:{} neighbor_dist:{} origin to {}:{}".format(cur_node, neighbor_node, neighbor_distance_from_cur, neighbor_node, neighbor_dist_from_origin))
        if distance_cache[neighbor_node] == None:
            distance_cache[neighbor_node] = neighbor_dist_from_origin
            found_conflicts = try_dfs_fill_distance(graph, neighbor_node, neighbor_dist_from_origin, distance_cache)
        else:
            if distance_cache[neighbor_node] != neighbor_dist_from_origin:
                #print("{} {} {}".format((distance_cache[neighbor_node] == None), distance_cache[neighbor_node], neighbor_dist_from_origin))
                found_conflicts = True

        if found_conflicts:
            break

    return found_conflicts

if __name__ == '__main__':
    n, m = list(map(int, input().split(" ")))
    graph = [[] for _ in range(n + 1)]
    for _ in range(m):
        l, r, d = list(map(int, input().split()))
        graph[l].append((r, d))
        graph[r].append((l, -d))

    distance_cache = [None for _ in range(n + 1)]
    has_conflict = False
    for i in range(1, len(distance_cache)):
        if distance_cache[i] == None:
            distance_cache[i] = 0
            has_conflict = try_dfs_fill_distance(graph, i, 0, distance_cache)
            if has_conflict:
                break

    print("No" if has_conflict else "Yes")