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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

const Node = function (val) {
  this.val = val;
  this.parent = this;
  this.rank = 1;
  this.weight = 0; // 親に対してのweight
};

const WeightedDisjointSet = function () {
  this.m = [];
};

WeightedDisjointSet.prototype.add = function (val) {
  this.m[val] = new Node(val);
};

WeightedDisjointSet.prototype.merge = function (val1, val2, weight) {
  const p1 = this.find(val1);
  const p2 = this.find(val2);
  const w1 = this.weight(val1);
  const w2 = this.weight(val2);
  if (p1 === p2) {
    if (w2 - w1 !== weight) {
      throw Error("invalid weight");
    }
    return;
  }
  if (p1.rank <= p2.rank) {
    if (p1.rank == p2.rank) {
      p2.rank++;
    }
    p1.parent = p2;
    p1.weight = -weight + w1 - w2;
  } else {
    p2.parent = p1;
    p2.weight = weight - w1 + w2;
  }
};

WeightedDisjointSet.prototype.find = function (val) {
  let cur = this.m[val];
  if (cur.parent != cur) {
    const root = this.find(cur.parent.val);
    cur.weight += cur.parent.weight;
    cur.parent = root;
  }
  return cur.parent;
};

WeightedDisjointSet.prototype.diff = function (val1, val2) {
  const p1 = this.find(val1);
  const p2 = this.find(val2);
  if (p1 != p2) {
    return null;
  }
  return this.weight(val2) - this.weight(val1);
};

WeightedDisjointSet.prototype.weight = function (val) {
  let weight = 0;
  let cur = this.m[val];
  while (cur.parent != cur) {
    weight += cur.weight;
    cur = cur.parent;
  }
  return weight;
};

let input = require("fs").readFileSync("/dev/stdin", "utf8");
const lines = input.trim().split("\n");
let n, m, d;

try {
  for (let i = 0; i < lines.length; i++) {
    if (i === 0) {
      [n, m] = lines[i].split(" ");
      d = new WeightedDisjointSet();
      for (let i = 0; i < n; i++) {
        d.add(i);
      }
    } else {
      const [x, y, w] = lines[i].split(" ").map((v) => parseInt(v));
      d.merge(x - 1, y - 1, w);
    }
  }
} catch (err) {
  console.log("No");
  return;
}
console.log("Yes");