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 (2.3.3) (judge verdict: Time Limit Exceeded)

def f(l,r)
	@c.each{|ary|
		if(ary[0] == l && ary[1] == r)
			return ary[2]
		end
	}
	nil
end

def set(l,r,d)
	if(f(l,r) && f(l,r) != d)
		raise
	else
		ary = [l,r,d]
		@c.push(ary)
	end
end

def check(l,r,d,t,h)
	if(h.include?(l))
		return
	else
		h.push(l)
	end

	# p "check stt:" + l.to_s + ".." + r.to_s + "(" + d.to_s + ")" + "  root:" + h.to_s + " sum:" + t.to_s

	@c.each{|a|
		if(a[0] == l)
			# p "next:" + a[1].to_s + "  from:" + t.to_s + " to:" + (t + a[2]).to_s
			if(a[1] == r)
				if(t + a[2] != d)
					raise
				end
				return
			else
				# 再帰
				check(a[1],r,d,t + a[2],h)
			end
		end
	}
end

n,m = gets.split.map(&:to_i)

@c = []

begin
m.times{
	l,r,d = gets.split.map(&:to_i)

	check(l,r,d,0,[])

	set(l,r,d)
	set(r,l,d * -1)
}
	puts "Yes"
rescue
	puts "No"
end