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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
typedef struct unionFindi{ //118
	unsigned *par;
	unsigned *rank;
	unsigned *num;
	int *pot;
}UFi;
void ufi_init(UFi *uf,int n){
	int i;
	uf->par=(unsigned*)malloc(sizeof(unsigned)*n);
	uf->rank=(unsigned*)malloc(sizeof(unsigned)*n);
	uf->num=(unsigned*)malloc(sizeof(unsigned)*n);
	uf->pot=(signed*)malloc(sizeof(signed)*n);
	for(i=0;i<n;i++){
		uf->par[i]=i;
		uf->rank[i]=0;
		uf->num[i]=1;
		uf->pot[i]=0;
	}
}
unsigned ufi_root(UFi *uf,int n){
	while(n!=uf->par[n]){
		uf->pot[n]+=uf->pot[uf->par[n]];
		uf->pot[uf->par[n]]+=uf->pot[uf->par[uf->par[n]]];
		uf->par[uf->par[n]]=uf->par[uf->par[uf->par[n]]];
		n=(uf->par[n]=uf->par[uf->par[n]]);
	}

	return n;
}
unsigned ufi_num(UFi *uf,int n){
	while(n!=uf->par[n]){
		uf->pot[n]+=uf->pot[uf->par[n]];
		uf->pot[uf->par[n]]+=uf->pot[uf->par[uf->par[n]]];
		uf->par[uf->par[n]]=uf->par[uf->par[uf->par[n]]];
		n=(uf->par[n]=uf->par[uf->par[n]]);
	}
	return uf->num[n];
}
unsigned ufi_same(UFi *uf,int n,int m){
	while(n!=uf->par[n]){
		uf->pot[n]+=uf->pot[uf->par[n]];
		uf->pot[uf->par[n]]+=uf->pot[uf->par[uf->par[n]]];
		uf->par[uf->par[n]]=uf->par[uf->par[uf->par[n]]];
		n=(uf->par[n]=uf->par[uf->par[n]]);
	}
	while(m!=uf->par[m]){
		uf->pot[m]+=uf->pot[uf->par[m]];
		uf->pot[uf->par[m]]+=uf->pot[uf->par[uf->par[m]]];
		uf->par[uf->par[m]]=uf->par[uf->par[uf->par[m]]];
		m=(uf->par[m]=uf->par[uf->par[m]]);
	}
	return n==m;
}
int ufi_weight(UFi *uf, int n){
	int ans=0;
	while(n!=uf->par[n]){
		uf->pot[n]+=uf->pot[uf->par[n]];
		uf->pot[uf->par[n]]+=uf->pot[uf->par[uf->par[n]]];
		uf->par[uf->par[n]]=uf->par[uf->par[uf->par[n]]];
		uf->par[n]=uf->par[uf->par[n]];
		ans+=uf->pot[n];
		n=uf->par[n];
	}
	return ans;
}
int ufi_diff(UFi *uf,int n,int m){
	int nw=0,mw=0;
	while(n!=uf->par[n]){
		uf->pot[n]+=uf->pot[uf->par[n]];
		uf->pot[uf->par[n]]+=uf->pot[uf->par[uf->par[n]]];
		uf->par[uf->par[n]]=uf->par[uf->par[uf->par[n]]];
		uf->par[n]=uf->par[uf->par[n]];
		nw+=uf->pot[n];
		n=uf->par[n];
	}
	while(m!=uf->par[m]){
		uf->pot[m]+=uf->pot[uf->par[m]];
		uf->pot[uf->par[m]]+=uf->pot[uf->par[uf->par[m]]];
		uf->par[uf->par[m]]=uf->par[uf->par[uf->par[m]]];
		uf->par[m]=uf->par[uf->par[m]];
		mw+=uf->pot[m];
		m=uf->par[m];
	}
	return mw-nw;
}
void ufi_unit(UFi *uf,int n,int m,int w){
	int nw=0,mw=0;
	while(n!=uf->par[n]){
		uf->pot[n]+=uf->pot[uf->par[n]];
		uf->pot[uf->par[n]]+=uf->pot[uf->par[uf->par[n]]];
		uf->par[uf->par[n]]=uf->par[uf->par[uf->par[n]]];
		uf->par[n]=uf->par[uf->par[n]];
		nw+=uf->pot[n];
		n=uf->par[n];
	}
	while(m!=uf->par[m]){
		uf->pot[m]+=uf->pot[uf->par[m]];
		uf->pot[uf->par[m]]+=uf->pot[uf->par[uf->par[m]]];
		uf->par[uf->par[m]]=uf->par[uf->par[uf->par[m]]];
		uf->par[m]=uf->par[uf->par[m]];
		mw+=uf->pot[m];
		m=uf->par[m];
	}
	if(n!=m){
		if(uf->rank[n]<uf->rank[m]){
			uf->par[n]=m;
			uf->num[m]+=uf->num[n];
			uf->pot[n]=mw-nw-w;
		}else{
			uf->par[m]=n;
			uf->num[n]+=uf->num[m];
			uf->pot[m]=w+nw-mw;
		}
		if(uf->rank[n]==uf->rank[m]){
			uf->rank[n]++;
		}
	}
}
int main(void){
	int n,m;
	int l,r,d;
	UFi uf;
	char flg=0;
	scanf("%d%d",&n,&m);
	ufi_init(&uf,n);
	while(m--){
		scanf("%d%d%d",&l,&r,&d);
		if(ufi_same(&uf,l,r)){
			if(ufi_diff(&uf,l,r)!=d) flg=1;
		}else{
			ufi_unit(&uf,l,r,d);
		}
	}
	if(flg){
		puts("No");
	}else{
		puts("Yes");
	}
	return 0;
}