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)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let (N, M): (usize, usize) = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap()
        )
    };
    let (L, R, D): (Vec<usize>, Vec<usize>, Vec<i64>) = {
        let (mut L, mut R, mut D) = (vec![], vec![], vec![]);
        for _ in 0..M {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            L.push(iter.next().unwrap().parse().unwrap());
            R.push(iter.next().unwrap().parse().unwrap());
            D.push(iter.next().unwrap().parse().unwrap());
        }
        (L, R, D)
    };

    let G = {
        let mut G = vec![std::collections::HashMap::new(); N + 1];
        for i in 0..M {
            G[L[i]].insert(R[i], D[i]);
            G[R[i]].insert(L[i], -D[i]);
        }
        G
    };
    const INF: i64 = 1_000_000_000_000_000;
    let mut x = vec![INF; N + 1];
    fn validate(i: usize, G: &Vec<std::collections::HashMap<usize, i64>>, x: &mut Vec<i64>) -> bool {
        let mut res = true;
        for (&j, &d) in &G[i] {
            if x[j] == INF {
                x[j] = x[i] + d;
                res &= validate(j, G, x);
            }
            else { res &= x[j] == x[i] + d }
        }
        res
    }

    let mut is_consistent = true;
    for i in 1..(N + 1) {
        if x[i] == INF {
            x[i] = 0;
            is_consistent &= validate(i, &G, &mut x);
        }
    }
    let ans = if is_consistent { "Yes" } else { "No" };

    println!("{}", ans);
}