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 Ruby (2.7.1) (judge verdict: Accepted)

class UnionFind
  def initialize(n)
    @n = n
    @par = Array.new(@n, -1)
    @dif = Array.new(@n, 0)
  end
  def find(x)
    @par[x] < 0 ? [x, 0] : (a, b = find(@par[x]); [@par[x] = a, @dif[x] += b])
  end
  def union(a, b, d)
    (pa, da), (pb, db) = find(a), find(b)
    return true if pa == pb && db-da == d
    return false if pa == pb
    if pa < pb then
      @par[pa] += @par[pb]
      @par[pb] = pa
      @dif[pb] += da-db+d
    else
      @par[pb] += @par[pa]
      @par[pa] = pb
      @dif[pa] += db-da-d
    end
    true
  end
end

N, M = gets.chomp.split(" ").map(&:to_i)
P = Array.new(M).map{gets.chomp.split(" ").map(&:to_i)}

uf = UnionFind.new(N)
ans = 'Yes'
P.each{|l, r, d|
  (ans = 'No'; break) if not uf.union(l-1, r-1, d)
}

puts ans