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: Wrong Answer)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use algo::*;
use std::collections::HashMap;

fn solve(n: usize, m: usize, lrds: Vec<[i32; 3]>) -> bool {
    let mut indices = HashMap::new();
    for [l, r, _] in &lrds {
        indices.insert(l, 0);
        indices.insert(r, 0);
    }

    let indices_clone = indices.clone();
    let mut xs = indices_clone.keys().collect::<Vec<_>>();
    xs.sort();

    for i in 0..xs.len() {
        indices.insert(xs[i], i);
    }

    let mut dists = HashMap::new();
    let mut graph = vec![Vec::new(); n];
    let mut weights = vec![None; n];

    for [l, r, d] in &lrds {
        dists.insert((indices[&l], indices[&r]), *d);
        dists.insert((indices[&r], indices[&l]), -d);

        if l < r {
            graph[indices[&l]].push(indices[&r]);
        } else {
            graph[indices[&r]].push(indices[&l]);
        }
    }

    weights[0] = Some(0);

    let mut visited = vec![false; n];

    fn rec(
        graph: &Vec<Vec<usize>>,
        dists: &HashMap<(usize, usize), i32>,
        weights: &mut Vec<Option<i32>>,
        visited: &mut Vec<bool>,
        e: usize,
    ) -> bool {
        if visited[e] {
            return true;
        }

        visited[e] = true;

        for t in &graph[e] {
            if let Some(w) = weights[*t] {
                if weights[e].unwrap() + dists[&(e, *t)] != w {
                    return false;
                }
            } else {
                weights[*t] = Some(weights[e].unwrap() + dists[&(e, *t)]);
            }

            if !rec(graph, dists, weights, visited, *t) {
                return false;
            }
        }

        true
    }

    rec(&graph, &dists, &mut weights, &mut visited, 0)
}

fn main() {
    input! {
        n: usize,
        m: usize,
        lrds: [[i32; 3]; m],
    }

    println!(
        "{}",
        if solve(
            n,
            m,
            lrds.into_iter()
                .map(|v| [v[0] - 1, v[1] - 1, v[2]])
                .collect()
        ) {
            "Yes"
        } else {
            "No"
        }
    );
}
*/

fn main() {
    let exe = "/tmp/binC529BF59";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";