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;

#define rep(i,s,n) for (int i = (int)s; i < (int)n; i++)
#define ll long long
#define ld long double
#define pb push_back
#define eb emplace_back
#define All(x) x.begin(), x.end()
#define Range(x, i, j) x.begin() + i, x.begin() + j
#define lbidx(x, y) lower_bound(x.begin(), x.end(), y) - x.begin()
#define ubidx(x, y) upper_bound(x.begin(), x.end(), y) - x.begin()
#define llbidx(x, y, z) lower_bound(x.begin(), x.end(), z) - lower_bound(x.begin(), x.end(), y) // 二要素間の距離
#define deg2rad(deg) ((((double)deg)/((double)360)*2*M_PI))
#define rad2deg(rad) ((((double)rad)/(double)2/M_PI)*(double)360)
#define Find(set, element) set.find(element) != set.end()
#define Decimal(x) printf("%.10f\n", x) // 小数点を10桁まで表示
// debug用
#define PrintVec(x) for (auto elementPrintVec: x) { cout << elementPrintVec << " "; } cout << "\n";
#define debug(x) cerr << #x << ": " << (x) << "\n";
#define endl "\n"
// gcj print用
#define Case(x) printf("Case #%d: ", x);

typedef pair<int, int> PI;
typedef pair<ll, ll> PLL;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<vector<vector<int>>> vvvi;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef vector<vector<vector<int>>> vvvl;
typedef vector<PI> vpi;
typedef vector<vector<PI>> vvpi;
typedef vector<vector<vector<PI>>> vvvpi;
typedef vector<PLL> vpl;
typedef vector<vector<PLL>> vvpl;
typedef vector<vector<vector<PLL>>> vvvpl;

int POWINT(int x, int n) {
  int ret = 1;
  while (n > 0) {
    if (n & 1) ret *= x;
    x *= x;
    n >>= 1;
  }
  return ret;
};

ll POWLL(ll x, int n) {
  ll ret = 1;
  while (n > 0) {
    if (n & 1) ret *= x;
    x *= x;
    n >>= 1;
  }
  return ret;
};

template<class T>
inline bool chmax(T &a, T b) {
  if(a < b) {
    a = b;
    return true;
  }
  return false;
};

template<class T>
inline bool chmin(T &a, T b) {
  if(a > b) {
    a = b;
    return true;
  }
  return false;
};

class ORD {
  public:
  int l, r, d, base;
  ORD() {}
  ORD(int l, int r, int d): l(l), r(r), d(d) {
    base = min(l, r);
  }

  bool operator < (const ORD &ord) const {
    return base < ord.base;
  }
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int N, M; cin >> N >> M;

  int l, r, d;
  vector<ORD> ords(M);
  rep(i, 0, M) {
    cin >> l >> r >> d;
    l--; r--;
    ords[i] = ORD(l, r, d);
  }

  sort(All(ords));

  bool ok = true;
  map<int, int> mp;
  rep(i, 0, M) {
    auto ord = ords[i];
    if (Find(mp, ord.l) && Find(mp, ord.r)) {
      if (mp[ord.r] - mp[ord.l] == ord.d) continue;
      else {
        ok = false;
        break;
      }
    } else if (Find(mp, ord.l)) {
      mp[ord.r] = mp[ord.l] + ord.d;
    } else if (Find(mp, ord.r)) {
      mp[ord.l] = mp[ord.r] - ord.d;
    } else {
      mp[ord.l] = 0;
      mp[ord.r] = ord.d;
    }
  }

  if (ok) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }

  return 0;
};