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)

#87D cleaned …確実にLTE食らう
N,M = map(int, input().split())

#iの番号を合わせるのに、最初に不要だけど、値を入れておく。
L_list=[0]
R_list=[0]
D_list=[0]

#LRD_listを初期化
#[n][0]:値入力済みのもののset　、　[n][m (m>0)]:n→mの変位
LRD_list = [["?"] * (N+1) for i in range(N+1)]
for i in range(N+1):
    LRD_list[i][0] = set()
    LRD_list[i][i] = 0 #自分→自分の変位は0

for i in range(1,M+1): #M < 2*10**5
    #print("#########################")
    L,R,D = map(int, input().split())
    
    if LRD_list[L][R] == "?" or  LRD_list[L][R] == D:
        if  LRD_list[L][R] == "?":
            LRD_list[L][R] = D
            LRD_list[R][L] = -D
            
            #print(L,"→",R,":",D)
            #print(R,"→",L,":",-D)
            
            for j in LRD_list[L][0]:
                LRD_list[R][j] = -D + LRD_list[L][j] #R→L→j
                LRD_list[R][0].add(j)
                LRD_list[j][R] = - LRD_list[L][j] + D #j→L→R
                LRD_list[j][0].add(R)
                
                #print(R,"→",j,":",- LRD_list[L][R] + LRD_list[L][j])
                #print(j,"→",R,":",- LRD_list[L][j] + LRD_list[L][R])
                
            LRD_list[L][0].add(R)
            
            for j in LRD_list[R][0]:
                LRD_list[L][j] = D + LRD_list[R][j] #L→R→j
                LRD_list[L][0].add(j)
                LRD_list[j][L] = - LRD_list[R][j] -D #j→R→L
                LRD_list[j][0].add(L)
                
                #print(L,"→",j,":",- LRD_list[R][L] + LRD_list[R][j])
                #print(j,"→",L,":",- LRD_list[R][j] + LRD_list[R][L])
                
            LRD_list[R][0].add(L)              
    else: # LRD_list[L][R] != "?" and  LRD_list[L][R] != D
        #print(L,"→",R,"=",LRD_list[L][R],".Not ",D)
        print("No")
        break
else:
    print("Yes")

#print("final:LRD_list")
#print(LRD_list)