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 = 1e9;
long long n, m, L, s, t;
vector<vector<pair<long long, long long> > > g;
long long Dijkstra() {
  vector<long long> dist(n, INF);
  set<pair<long long, long long> > q;
  dist[s] = 0;
  q.insert({0, s});
  while (!q.empty()) {
    long long v = q.begin()->second;
    q.erase(q.begin());
    for (long long i = 0; i < (long long)(g[v]).size(); i++) {
      long long to = g[v][i].first, w = g[v][i].second;
      if (dist[to] > dist[v] + w) {
        q.erase({dist[to], to});
        dist[to] = dist[v] + w;
        q.insert({dist[to], to});
      }
    }
  }
  return dist[t];
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cin >> n >> m >> L >> s >> t;
  vector<pair<long long, long long> > specEdgs;
  g.resize(n);
  for (long long i = 0; i < m; i++) {
    long long v, u, w;
    cin >> v >> u >> w;
    if (w == 0) {
      w = INF;
      specEdgs.push_back({v, (long long)(g[v]).size()});
    }
    g[v].push_back({u, w});
  }
  if (Dijkstra() < L) {
    cout << "NO\n";
    return 0;
  }
  for (long long i = 0; i < (long long)(specEdgs).size(); i++) {
    long long v = specEdgs[i].first, j = specEdgs[i].second;
    g[v][j].second = 1;
  }
  long long len = Dijkstra();
  if (len > L) {
    cout << "NO\n";
    return 0;
  }
  for (long long i = 0; i < (long long)(specEdgs).size(); i++) {
    long long v = specEdgs[i].first, j = specEdgs[i].second;
    g[v][j].second += L - len;
    len = Dijkstra();
    if (len == L) {
      break;
    }
  }
  cout << "YES\n";
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < (long long)(g[i]).size(); j++) {
      cout << i << ' ' << g[i][j].first << ' ' << g[i][j].second << '\n';
    }
  }
  return 0;
}
