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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_macros, dead_code)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros, dead_code)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros, dead_code)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(dead_code)]
struct UnionFind {
    parent: Vec<usize>,
    rank: Vec<usize>,
    size: Vec<usize>,
}

#[allow(dead_code)]
impl UnionFind {
    fn new(n: usize) -> UnionFind {
        let mut p = vec![0; n];
        for i in 0..n {
            p[i] = i;
        }
        return UnionFind {
            parent: p,
            rank: vec![0; n],
            size: vec![1; n],
        };
    }

    fn find(&mut self, x: usize) -> usize {
        if x == self.parent[x] {
            x
        } else {
            let p = self.parent[x];
            let pr = self.find(p);
            self.parent[x] = pr;
            pr
        }
    }

    fn same(&mut self, a: usize, b: usize) -> bool {
        self.find(a) == self.find(b)
    }

    fn unite(&mut self, a: usize, b: usize) {
        let a_root = self.find(a);
        let b_root = self.find(b);
        if a_root == b_root {
            return;
        }
        if self.rank[a_root] > self.rank[b_root] {
            self.parent[b_root] = a_root;
            self.size[a_root] += self.size[b_root];
        } else {
            self.parent[a_root] = b_root;
            self.size[b_root] += self.size[a_root];
            if self.rank[a_root] == self.rank[b_root] {
                self.rank[b_root] += 1;
            }
        }
    }

    fn get_size(&mut self, x: usize) -> usize {
        let root = self.find(x);
        self.size[root]
    }
}

const MOD_P: usize = 1000000007;

#[allow(dead_code)]
// fact(n) = n! mod p
fn fact(n: usize) -> usize {
    let mut acc = 1;
    for i in 1..n + 1 {
        acc = acc * i % MOD_P;
    }
    acc
}

#[allow(dead_code)]
fn mod_pow(b: usize, mut e: usize) -> usize {
    let mut base = b;
    let mut acc = 1;

    while e > 1 {
        if e % 2 == 1 {
            acc = acc * base % MOD_P;
        }
        e /= 2;
        base = base * base % MOD_P;
    }

    if e == 1 {
        acc = acc * base % MOD_P;
    }

    acc
}

#[allow(dead_code)]
fn comb(n: usize, r: usize) -> usize {
    // nCr = n! / (r! (n-r)!) = n! (r!)^(p-2) ((n-r)!)^(p-2)
    let x = ((n - r + 1)..(n + 1)).fold(1, |p, x| p * x % MOD_P);
    let y = mod_pow(fact(r), MOD_P - 2);
    x * y % MOD_P
}

#[derive(Clone, Copy, Debug)]
struct GF(usize);

impl std::ops::Add for GF {
    type Output = GF;
    fn add(self, rhs: GF) -> Self::Output {
        let mut d = self.0 + rhs.0;
        if d >= MOD_P {
            d -= MOD_P;
        }
        GF(d)
    }
}

impl std::ops::AddAssign for GF {
    fn add_assign(&mut self, rhs: GF) {
        *self = *self + rhs;
    }
}

impl std::ops::Sub for GF {
    type Output = GF;
    fn sub(self, rhs: GF) -> Self::Output {
        let mut d = self.0 + MOD_P - rhs.0;
        if d >= MOD_P {
            d -= MOD_P;
        }
        GF(d)
    }
}

impl std::ops::SubAssign for GF {
    fn sub_assign(&mut self, rhs: GF) {
        *self = *self - rhs;
    }
}

impl std::ops::Mul for GF {
    type Output = GF;
    fn mul(self, rhs: GF) -> Self::Output {
        let mut d = self.0 * rhs.0;
        d %= MOD_P;
        GF(d)
    }
}

impl std::ops::MulAssign for GF {
    fn mul_assign(&mut self, rhs: GF) {
        *self = *self * rhs;
    }
}

impl std::fmt::Display for GF {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

#[allow(dead_code)]
impl GF {
    pub fn new(n: usize) -> GF {
        GF(n % MOD_P)
    }
    pub fn zero() -> GF {
        GF(0)
    }
    pub fn one() -> GF {
        GF(1)
    }
    pub fn pow(self, mut e: usize) -> GF {
        let mut acc = GF::one();
        let mut b = self;
        while e > 1 {
            if e % 2 == 1 {
                acc *= b;
            }
            b *= b;
            e /= 2;
        }
        if e == 1 {
            acc *= b;
        }
        acc
    }
    pub fn fact(self) -> GF {
        let mut acc = GF::one();
        for i in 1..=self.0 {
            acc *= GF::new(i);
        }
        acc
    }
    pub fn inv(self) -> GF {
        self.pow(MOD_P - 2)
    }
    pub fn comb(n: GF, r: GF) -> GF {
        // nCr = n! / (r! (n-r)!) = n! (r!)^(p-2) ((n-r)!)^(p-2)
        let x = ((n.0 - r.0 + 1)..=n.0).fold(GF::one(), |p, x| p * GF(x));
        let y = r.fact().inv();
        x * y
    }
}

#[allow(dead_code)]
#[derive(Debug)]
struct MemComb {
    inv: Vec<GF>,
    fact: Vec<GF>,
    factinv: Vec<GF>,
}

#[allow(dead_code)]
impl MemComb {
    pub fn new(n: usize) -> MemComb {
        let mut inv = vec![GF::one(); n + 1];
        let mut fact = vec![GF::one(); n + 1];
        let mut factinv = vec![GF::one(); n + 1];

        for i in 2..=n {
            fact[i] = fact[i - 1] * GF(i);
        }

        factinv[n] = fact[n].inv();
        for i in (1..n).rev() {
            factinv[i] = factinv[i + 1] * GF(i + 1); // 1/n! = 1/(n+1)! * (n+1)
            inv[i] = factinv[i] * fact[i - 1]; // 1/n = 1/n! * (n-1)!
        }
        inv[n] = factinv[n] * fact[n - 1];

        MemComb { inv, fact, factinv }
    }
}

#[allow(dead_code)]
fn gcd(a: usize, b: usize) -> usize {
    if b > a {
        gcd(b, a)
    } else if a % b == 0 {
        b
    } else {
        gcd(b, a % b)
    }
}

#[allow(dead_code)]
fn getline() -> String {
    let mut __ret = String::new();
    std::io::stdin().read_line(&mut __ret).ok();
    return __ret;
}

#[allow(unused_imports)]
use std::cmp::{max, min};

fn main() {
    input! {
        n: usize,
        m: usize,
        lrd: [(usize1,usize1,isize); m],
    }
    let mut g = vec![Vec::new(); n];
    for &(l, r, d) in &lrd {
        g[l].push((r, d));
        g[r].push((l, -d));
    }

    let mut dist = vec![None; n];
    for i in 0..n {
        if dist[i] == None {
            dist[i] = Some(0 as isize);
            let mut deq = std::collections::VecDeque::new();
            for &(next, d) in &g[i] {
                deq.push_back((next, d));
            }

            while !deq.is_empty() {
                let (next, d) = deq.pop_front().unwrap();
                match dist[next] {
                    Some(d2) if d != d2 => {
                        println!("No");
                        return;
                    }
                    Some(_) => {}
                    None => {
                        dist[next] = Some(d);
                        for &(nextnext, nextd) in &g[next] {
                            deq.push_back((nextnext, d + nextd));
                        }
                    }
                }
            }
        }
    }
    // let mut ans = 0;
    println!("Yes");
}