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 <algorithm>
#include <cassert>
#include <iostream>
#include <map>
#include <vector>

static const int IINF = 1 << 30;
static const long long LINF = 1LL << 60;
static const long long MOD = 1.0e+9 + 7;

template <typename T> std::vector<T> vectors(std::size_t n, T val) {
  return std::vector<T>(n, val);
}

template <typename T, typename... Args>
auto vectors(std::size_t n, Args... args) {
  return std::vector<decltype(vectors<T>(args...))>(n, vectors<T>(args...));
}

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

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

template <class T> inline void chadd(T &a, const T &b) {
  a += b, a %= MOD;
  // TODO minus case
}

template <class T>
std::ostream &operator<<(std::ostream &s, const std::vector<T> &v) {
  if (v.empty())
    return s;
  s << *v.begin();
  for (auto iter = v.begin() + 1; iter != v.end(); ++iter)
    if (std::is_fundamental<T>::value)
      s << " " << *iter;
    else
      s << std::endl << *iter;
  return s;
}

int main() {
  // Input
  int N, M;
  std::cin >> N >> M;
  std::vector<int> L(M);
  std::vector<int> R(M);
  std::vector<int> D(M);
  for (int i = 0; i < M; ++i) {
    std::cin >> L[i] >> R[i] >> D[i];
    --L[i], --R[i];
  }

  // Main
  std::vector<int> dist(N, IINF);
  bool res = true;
  for (int i = 0; i < M; ++i) {
    if (dist[L[i]] == IINF and dist[R[i]] == IINF) {
      dist[L[i]] = 0;
      dist[R[i]] = D[i];
      continue;
    }
    if (dist[R[i]] == IINF) {
      dist[R[i]] = dist[L[i]] + D[i];
      continue;
    }
    if (dist[L[i]] == IINF) {
      dist[L[i]] = dist[R[i]] - D[i];
      continue;
    }
    if (dist[R[i]] - dist[L[i]] != D[i]) {
      // std::cout << dist[L[i]] - dist[R[i]] << std::endl;
      // std::cout << D[i] << std::endl;
      res = false;
      break;
    }
  }

  if (res)
    std::cout << "Yes" << std::endl;
  else
    std::cout << "No" << std::endl;

  return 0;
}