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;
const long long INF = 1000000000000;
int n, m;
struct edge_t {
  long long v, w, edit, orig;
};
vector<vector<edge_t>> g;
vector<pair<int, int>> p;
void sp(int s) {
  vector<long long> d(n, INF);
  d[s] = 0;
  set<pair<int, int>> q;
  q.insert(make_pair(d[s], s));
  while (!q.empty()) {
    int v = q.begin()->second;
    q.erase(q.begin());
    for (size_t j = 0; j < g[v].size(); ++j) {
      int to = g[v][j].v, len = g[v][j].w;
      if (d[v] + len < d[to]) {
        q.erase(make_pair(d[to], to));
        d[to] = d[v] + len;
        p[to] = make_pair(v, j);
        q.insert(make_pair(d[to], to));
      }
    }
  }
}
int main() {
  int l, s, t;
  cin >> n >> m >> l >> s >> t;
  g.resize(n + 1);
  p.resize(n + 1);
  for (int i = 0; i < m; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    edge_t edge;
    edge.v = v;
    edge.w = w;
    edge.edit = !w;
    if (edge.edit) {
      edge.w = 1;
    }
    edge.orig = true;
    g[u].push_back(edge);
    edge.v = u;
    edge.orig = false;
    g[v].push_back(edge);
  }
  while (true) {
    sp(s);
    long long len = 0;
    pair<int, int> pos(-1, -1);
    int tt = t;
    while (tt != s) {
      auto prev = p[tt];
      len += g[prev.first][prev.second].w;
      if (g[prev.first][prev.second].edit) {
        pos = prev;
      }
      tt = prev.first;
    }
    if (len == l) {
      cout << "YES" << endl;
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < g[i].size(); j++) {
          if (g[i][j].orig) {
            cout << i << " " << g[i][j].v << " " << g[i][j].w << endl;
          }
        }
      }
      exit(0);
    } else if (len > l) {
      cout << "NO" << endl;
      break;
    } else if (pos.first == -1) {
      cout << "NO" << endl;
      break;
    }
    g[pos.first][pos.second].w += l - len;
  }
}
