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(unused_macros, unused_imports, dead_code)]

use std::io;
use std::process;

fn read_line() -> String {
    let mut s = String::new();
    io::stdin().read_line(&mut s).unwrap();
    s
}

macro_rules! reads {
    ($($t:ty),+) => {
        {
            let line = read_line();
            let mut it = line.trim().split_whitespace();
            let result = (
                $(it.next().unwrap().parse::<$t>().unwrap(),)+
            );
            assert!(it.next().is_none());
            result
        }
    };
}

fn read_vec() -> Vec<i64> {
    let line = read_line();
    let it = line.trim().split_whitespace();
    it.map(|s| s.parse().unwrap()).collect()
}

fn main() {
    let INF: i64 = 10i64.pow(10);

    let (N, M) = reads!(usize, usize);
    let mut edges = vec![vec![]; N];

    for _ in 0..M {
        let (mut L, mut R, D) = reads!(usize, usize, i64);
        L = L-1; R = R-1;
        edges[L].push((R, D));
        edges[R].push((L, -D));
    }

    let mut visited = vec![false; N];
    let mut place = vec![0; N];

    fn walk(i: usize, mut visited: &mut Vec<bool>, mut place: &mut Vec<i64>, edges: &Vec<Vec<(usize, i64)>>) {
        if visited[i] {
            return;
        }
        visited[i] = true;
        for &(j, d) in &edges[i] {
            if visited[j] && (place[j] != place[i] + d) {
                println!("No");
                process::exit(0);
            }
            place[j] = place[i] + d;
            walk(j, &mut visited, &mut place, &edges);
        }
    }

    for i in 0..N {
        if !visited[i] {
            place[i] = 0;
            walk(i, &mut visited, &mut place, &edges);
        }
    }

    println!("Yes");
}