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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<cstdio>
using namespace std;
const int N=100100,M=400400;
int i,j,k,n,m,ch,ff,Fg,En;
int a[N],h[N],z[N];
struct edge { int s,n,v;} E[M];
void R(int &x) {
	ff=x=0;ch=getchar();
	while (ch<'0' || '9'<ch) { if (ch=='-') ff=1;ch=getchar();}
	while ('0'<=ch && ch<='9') x=x*10+ch-'0',ch=getchar();
	if (ff) x=-x;
}
void W(int x) {
	if (x<0) putchar('-'),x=-x;
	if (x>=10) W(x/10);
	putchar(x%10+'0');
}
void E_add(int x,int y,int v) {
	E[++En].s=y;E[En].v=v;
	E[En].n=h[x];h[x]=En;
	E[++En].s=x;E[En].v=-v;
	E[En].n=h[y];h[y]=En;
}
void dfs(int x) {
	z[x]=1;
	for (int k=h[x];k;k=E[k].n) {
		if (!z[E[k].s]) {
			a[E[k].s]=a[x]+E[k].v;
			dfs(E[k].s);
		}
		else {
			if (a[E[k].s]!=a[x]+E[k].v) Fg=1;
		}
	}
}
int main() {
	R(n);R(m);
	for (i=1;i<=m;i++) {
		int x,y,v;
		R(x);R(y);R(v);
		E_add(x,y,v);
	}
	for (i=1;i<=n;i++) if (!z[i]) dfs(i);
	if (Fg) puts("No");
	else puts("Yes");
}