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 Rust (1.15.1) (judge verdict: Accepted)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;
use std::collections::VecDeque;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

//return true if consistent
fn search(graph: &mut Vec<Vec<(usize, i64)>>, people: &mut Vec<i64>, i: usize) -> bool{
    let mut queue: VecDeque<(usize)> = VecDeque::new();
    queue.push_back(i);
    let dummy = std::i64::MAX;
    while let Some(cur_v) = queue.pop_front(){
        while let Some((next_v, d)) = graph[cur_v].pop(){
            if people[next_v] == dummy{
                people[next_v] = people[cur_v] + d;
                queue.push_back(next_v);
            }else if people[next_v] != people[cur_v] + d{
                return false;
            }
        }
    }
    true
}

fn main(){
    let line = read_as_vec::<usize>();
    let (n, m) = (line[0], line[1]);
    let dummy = std::i64::MAX;
    let mut graph: Vec<Vec<(usize, i64)>> = vec![vec![];n];
    let mut people: Vec<i64> = vec![dummy; n];
    for _ in 0..m{
        let line = read_as_vec::<usize>();
        //let (l, r, d) = (cmp::min(line[0], line[1]), cmp::max(line[0], line[1]), line[2]);
        let (l, r, d) = (line[0]-1, line[1]-1, line[2] as i64);
        graph[l].push((r, d));
        graph[r].push((l, -d));
    }

    for i in 0..n{
        if graph[i].len() == 0{
            continue;
        }
        //init people[i] position to 0
        people[i] = 0;
        let is_consisent: bool = search(&mut graph, &mut people, i);

        if !is_consisent{
            println!("No");
            return;
        }

    }

    println!("Yes");

}