7 9 999999999 0 3
0 1 0
1 2 0
2 3 0
0 4 1
4 1 1
1 5 499999999
5 2 499999999
2 6 1
6 3 1
 7 9 320 0 3
0 1 0
1 2 0
2 3 0
0 4 1
4 1 1
1 5 100
5 2 100
2 6 59
6 3 61
 4 5 7 0 3
0 1 0
1 2 3
2 3 0
0 2 5
1 3 5
 8 9 10 1 0
1 2 1
2 4 1
1 3 0
3 4 0
4 5 0
5 6 1
6 0 1
5 7 0
7 0 0
 4 4 14 1 3
1 3 13
2 3 0
2 0 0
1 0 12
 5 6 1000000000 0 4
0 1 1
2 0 2
3 0 3
4 1 0
4 2 0
3 4 0
 4 5 10 1 2
0 1 3
1 2 0
1 3 4
2 3 4
2 0 6
 4 4 2 1 3
1 3 13
2 3 0
2 0 0
1 0 0
 5 5 2 0 2
0 1 1
1 2 1
0 4 0
4 3 0
3 2 0
 5 5 3 0 2
0 1 1
1 2 1
0 4 0
4 3 0
3 2 0
 4 4 8 1 3
1 3 13
2 3 0
2 0 0
1 0 6
 1000 1 1000000000 998 0
0 999 0
 5 5 1 0 2
0 1 1
1 2 1
0 4 0
4 3 0
3 2 0
 100 1 123456 99 0
0 99 123456
 4 4 13 1 3
1 3 13
2 3 0
2 0 0
1 0 12
 7 9 319 0 3
0 1 0
1 2 0
2 3 0
0 4 1
4 1 1
1 5 100
5 2 100
2 6 59
6 3 61
 1000 1 5 999 0
0 999 0

YES
0 1 1
1 2 999999996
2 3 999999997
0 4 1
4 1 1
1 5 499999999
5 2 499999999
2 6 1
6 3 1
 YES
0 1 1
1 2 199
2 3 318
0 4 1
4 1 1
1 5 100
5 2 100
2 6 59
6 3 61
 YES
0 1 3
1 2 3
2 3 2
0 2 5
1 3 5
 YES
1 2 1
2 4 1
1 3 1
3 4 1
4 5 6
5 6 1
6 0 1
5 7 1
7 0 1
 NO YES
0 1 1
2 0 2
3 0 3
4 1 999999999
4 2 999999998
3 4 999999997
 NO NO YES
0 1 1
1 2 1
0 4 1
4 3 1
3 2 1
 NO YES
1 3 13
2 3 1
2 0 1
1 0 6
 NO NO YES
0 99 123456
 YES
1 3 13
2 3 1
2 0 1
1 0 12
 YES
0 1 1
1 2 198
2 3 317
0 4 1
4 1 1
1 5 100
5 2 100
2 6 59
6 3 61
 YES
0 999 5

#include <bits/stdc++.h>
using namespace std;
template <typename T>
T input() {
  T ans = 0, m = 1;
  char c = ' ';
  while (!((c >= '0' && c <= '9') || c == '-')) c = getchar();
  if (c == '-') m = -1, c = getchar();
  while (c >= '0' && c <= '9') {
    ans = ans * 10 + (c - '0'), c = getchar();
  }
  return ans * m;
}
template <typename T>
void read(T& a) {
  a = input<T>();
}
template <typename T, typename... R>
void read(T& a, R&... r) {
  a = input<T>();
  read(r...);
}
const int N = 1e3 + 12;
const int M = 1e4 + 12;
const long long INF = 2e18;
int x[M], y[M], w[M];
bool emp[M];
long long dist1[N], dist2[N];
vector<int> g[N];
int n, m, L, s, t;
long long need;
void dijk(long long* dist, bool fl) {
  priority_queue<pair<long long, int>, vector<pair<long long, int> >,
                 greater<pair<long long, int> > >
      q;
  dist[s] = 0;
  q.push({0, s});
  while (!q.empty()) {
    int v = q.top().second;
    long long d = q.top().first;
    q.pop();
    if (d > dist[v]) continue;
    for (auto i : g[v]) {
      int u = x[i] + y[i] - v;
      if (fl && emp[i] && d + w[i] < dist[u] && d + w[i] < dist1[u] + need) {
        w[i] = dist1[u] + need - d;
      }
      if (d + w[i] < dist[u]) {
        dist[u] = d + w[i];
        q.push({dist[u], u});
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  read(n, m, L, s, t);
  for (int i = 0; i < m; ++i) {
    read(x[i], y[i], w[i]);
    g[x[i]].push_back(i);
    g[y[i]].push_back(i);
    if (!w[i]) {
      emp[i] = w[i] = 1;
    }
  }
  for (int i = 0; i < n; ++i) {
    dist1[i] = dist2[i] = INF;
  }
  dijk(dist1, 0);
  if (dist1[t] > L) {
    cout << "NO\n";
    return 0;
  }
  need = L - dist1[t];
  dijk(dist2, 1);
  if (dist2[t] != L) {
    cout << "NO\n";
    return 0;
  }
  cout << "YES\n";
  for (int i = 0; i < m; ++i) {
    cout << x[i] << " " << y[i] << " " << w[i] << "\n";
  }
}
