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;
long long n, m, s, t, l, rest;
long long d[1010], d2[1010], w[10010];
bool zeredg[10010];
pair<long long, long long> edg[10010];
vector<vector<long long> > edglist;
void dijkstra(long long dist[], bool sec) {
  set<pair<long long, long long> > najbl;
  dist[s] = 0;
  najbl.insert({0, s});
  for (long long i = 0; i < n; ++i) {
    if (s != i) {
      dist[i] = 1e18;
      najbl.insert({dist[i], i});
    }
  }
  while (najbl.size()) {
    long long v = najbl.begin()->second;
    najbl.erase(najbl.begin());
    for (auto i : edglist[v]) {
      long long u = edg[i].first + edg[i].second - v;
      if (sec and dist[u] > dist[v] + w[i] and zeredg[i] and
          w[i] < d[u] + rest - dist[v]) {
        w[i] = d[u] + rest - dist[v];
      }
      if (dist[u] > dist[v] + w[i]) {
        najbl.erase({dist[u], u});
        dist[u] = dist[v] + w[i];
        najbl.insert({dist[u], u});
      }
    }
  }
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n >> m >> l >> s >> t;
  vector<long long> vi;
  edglist.resize(n, vi);
  for (long long i = 0; i < m; ++i) {
    long long u, v, e;
    cin >> u >> v >> e;
    edglist[u].push_back(i);
    edglist[v].push_back(i);
    edg[i] = {u, v};
    if (e) {
      w[i] = e;
    } else {
      w[i] = 1;
      zeredg[i] = 1;
    }
  }
  dijkstra(d, 0);
  if (d[t] > l) {
    cout << "NO";
    return 0;
  } else if (d[t] == l) {
    cout << "YES\n";
    for (long long i = 0; i < m; ++i) {
      cout << edg[i].first << " " << edg[i].second << " " << w[i] << "\n";
    }
    return 0;
  }
  rest = l - d[t];
  dijkstra(d2, 1);
  if (d2[t] != l) {
    cout << "NO\n";
    return 0;
  }
  cout << "YES\n";
  for (long long i = 0; i < m; ++i) {
    cout << edg[i].first << " " << edg[i].second << " " << w[i] << "\n";
  }
}
