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 (3.8.2) (judge verdict: Wrong Answer)

import sys
sys.setrecursionlimit(10**9)

read=sys.stdin.read
class Unionfind():
    def __init__(self,n):
        self.parents=[-1]*n
        self.dist=[0]*n 
    
    def find(self,x):
        if self.parents[x]<0:
            return x
        else:
            self.dist[x]+=max(0,self.dist[self.parents[x]])
            self.parents[x]=self.find(self.parents[x])
            return self.parents[x]
    
    def union(self,x,y,d):
        rx=self.find(x)
        ry=self.find(y)
        diff=max(0,self.dist[y])-max(0,self.dist[x])-d
        if rx==ry:
            if diff!=0:
                return True
            return False
        if diff<0:
            rx,ry=ry,rx
            diff=-diff
        self.parents[ry]=min(self.parents[ry],-diff+self.parents[rx])
        self.parents[rx]=ry
        self.dist[rx]=diff
        return False
    
    def showdist(self):
        retrun 
def main():
    n,m,*lrd=map(int,read().split())
    v=Unionfind(n)
    for l,r,d in zip(*[iter(lrd)]*3):
        if v.union(l-1,r-1,d):
            print('No')
            break
    else:
        if max(-d-1 for d in v.parents if d<0) >10**9:
            print('No')
        else:
            print('Yes')
if __name__=='__main__':
    main()