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;
int n, m, s, t, a, b;
long long L, w;
long long dist[1024];
int parent[1024];
int marked[1024][1024] = {0};
int check[1024][1024] = {0};
vector<pair<pair<int, long long>, long long> > graph;
vector<pair<int, long long> > g[1024];
void Dijkstra(int s, int t) {
  fill(parent, parent + n, -1);
  fill(dist, dist + n, 1e18 + 1);
  priority_queue<pair<long long, int>, vector<pair<long long, int> >,
                 greater<pair<long long, int> > >
      pq;
  dist[s] = 0;
  parent[s] = s;
  pq.push(pair<long long, int>(dist[s], s));
  while (!pq.empty()) {
    pair<long long, int> p = pq.top();
    pq.pop();
    int d = p.first;
    int a = p.second;
    for (int i = 0; i < g[a].size(); ++i) {
      int k = g[a][i].first;
      if (dist[k] > dist[a] + g[a][i].second) {
        dist[k] = dist[a] + g[a][i].second;
        parent[k] = a;
        pq.push(pair<long long, int>(dist[k], k));
      }
    }
  }
}
int main() {
  cin >> n >> m >> L >> s >> t;
  for (int i = 0; i < m; ++i) {
    cin >> a >> b >> w;
    if (w == 0) {
      marked[a][b] = 1;
      marked[b][a] = 1;
      w = 1;
    }
    g[a].push_back(make_pair(b, w));
    g[b].push_back(make_pair(a, w));
    graph.push_back(make_pair(pair<int, long long>(a, b), w));
  }
  Dijkstra(s, t);
  if (dist[t] > L) {
    cout << "NO" << endl;
  } else {
    while (dist[t] < L) {
      for (int i = 0; i < n; ++i)
        for (int j = 0; j < n; ++j) check[i][j] = 0;
      int x = t;
      int cnt = 0;
      long long diff = L - dist[t];
      while (parent[x] != x) {
        if (marked[parent[x]][x] == 1) {
          marked[parent[x]][x] = 1 + diff;
          marked[x][parent[x]] = 1 + diff;
          diff = 0;
          check[parent[x]][x] = 1;
          check[x][parent[x]] = 1;
        }
        x = parent[x];
      }
      if (diff > 0) {
        cout << "NO" << endl;
        return 0;
      }
      for (int i = 0; i < n; ++i) g[i].clear();
      for (int i = 0; i < graph.size(); ++i) {
        int a = graph[i].first.first;
        int b = graph[i].first.second;
        int w = graph[i].second;
        if (w == 1 && check[a][b])
          graph[i].second = marked[a][b];
        else if (w == 1 && !check[a][b] && marked[a][b])
          graph[i].second = L + 1, marked[a][b] = 0, marked[b][a] = 0;
        g[a].push_back(make_pair(b, graph[i].second));
        g[b].push_back(make_pair(a, graph[i].second));
      }
      Dijkstra(s, t);
    }
    if (dist[t] == L) {
      cout << "YES" << endl;
      for (int i = 0; i < graph.size(); ++i) {
        int a = graph[i].first.first;
        int b = graph[i].first.second;
        long long w = graph[i].second;
        cout << a << " " << b << " " << w << endl;
      }
    }
  }
  return 0;
}
