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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

N, M = map(int,input().split())
L = [0] * M
R = [0] * M
D = [0] * M
for i in range(M):
	L[i],R[i],D[i] = map(int,input().split())
#	print(L[i],R[i],D[i])
leftside = 0
cand = set()
for i in range(M):
	cand.add(L[i])
for i in range(M):
	if R[i] in cand:
		cand.remove(R[i])

res = True
if M == 0:
	res = True
else:
	if len(cand) == 0:
		res = False
	else:
		leftside = list(cand)
#		print("leftside:",leftside)
		ok = True
		for c in leftside:
			point = [-1] * (N+1)
			point[c] = 0
			ok = True
			while True:
				update = False
				for i in range(M):
					if point[L[i]] != -1:
						if point[R[i]] == -1:
							update = True
							point[R[i]] = point[L[i]] + D[i]
						else:
							if point[R[i]] != point[L[i]] + D[i]:
								ok = False
								break
				if update == False:
					break
				res &= ok
					
print("Yes" if res == True else "No")