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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;using ll=long long;using vi=vector<int>;using vvi=vector<vi>;using vl=vector<ll>;using vvl=vector<vl>;using P=pair<int,int>;using PL=pair<ll,ll>;using vp=vector<P>;using vpl=vector<PL>;
template<typename T>constexpr auto inf=numeric_limits<T>::max()/2;constexpr int INF=inf<int>,MOD=1000000007;constexpr ll LINF=inf<ll>;
#define _ol3(_1,_2,_3,name,...)name
#define _rep(i,n)_repi(i,0,n)
#define _repi(i,a,b)for(int i=a,i##_l=(b);i<i##_l;++i)
#define REP(...)_ol3(__VA_ARGS__,_repi,_rep,)(__VA_ARGS__)
#define REPR(i,n)for(int i=n-1;i>=0;--i)
#define REPA(i,v)REP(i,v.size())
#define all(v)(v).begin(),(v).end()
#define bit(n)(1ll<<(n))
#define uniq(v)sort(all(v));v.erase(unique(all(v)),v.end())
#define F first
#define S second
#define endl '\n'
#define cho(n,a,b)cout<<((n)?a:b)<<endl
void YES(int n){cho(n,"YES","NO");}void Yes(int n){cho(n,"Yes","No");}void Poss(int n){cho(n,"Possible","Impossible");}
void _print(ostream&){}template<class T,class...U>void _print(ostream&s,T&&t,U&&...u){s<<t<<(sizeof...(u)?' ':'\n');_print(s,u...);}
template<class...T>void print(T&&...t){_print(cout,t...);}
#ifndef LOCAL
struct osd{template<class T>osd&operator<<(const T&t){return*this;}};osd cer_;
#define dprint(...)
#define cerr cer_
#else
template<class...T>void dprint(T&&...t){_print(cerr,t...);}
#endif
template<class T>void chmax(T&a,const T&b){if(a<b)a=b;}template<class T>void chmin(T&a,const T&b){if(a>b)a=b;}
template<class T>ostream&operator<<(ostream&o,const vector<T>&v){for(auto&&i:v)o<<i<<' ';return o;}
template<class T>istream&operator>>(istream&i,vector<T>&v){for(T&j:v)i>>j;return i;}
template<class T,class U>ostream&operator<<(ostream&o,const pair<T,U>&p){return o<<p.F<<' '<<p.S;}
template<class T,class U>istream&operator>>(istream&i,pair<T,U>&p){return i>>p.F>>p.S;}
template<class T>ostream&operator<<(ostream&o,const set<T>&v){for(auto&&i:v)o<<i<<' ';return o;}
template<class T>ostream&operator<<(ostream&o,const multiset<T>&v){for(auto&&i:v)o<<i<<' ';return o;}
template<class T>vector<T>&operator<<(vector<T>&v,const T&t){v.push_back(t);return v;}
template<class T>set<T>&operator<<(set<T>&v,const T&t){v.insert(t);return v;}
template<class T>multiset<T>&operator<<(multiset<T>&v,const T&t){v.insert(t);return v;}

vp data;

int rt(int x){
    if(data[x].F==-1)return x;
    return rt(data[x].F);
}

int dif_rt(int x){
    if(data[x].F==-1)return 0;
    return dif_rt(data[x].F)+data[x].S;
}

int main(){
    cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(10);
    int n,m;
    cin>>n>>m;
    data.resize(n, P(-1, 0));
    /*
    [4byte:root][4byte:ofset]
     0xffffffff: null
     */
    REP(i,m){
        int l,r,d;
        cin>>l>>r>>d;
        l--;r--;
        if(rt(l)==rt(r)){
            if(dif_rt(l)+d!=dif_rt(r)){
                Yes(0);
                return 0;
            }else continue;
        }
        data[r]={l, d};
        dprint(data);
    }
    Yes(1);
    return 0;
}