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 = 1e18;
const int mod = 1e9 + 7;
const int N = 1e3 + 10;
bool vis[N];
long long dist[N], dis[N][N];
int par[N];
vector<int> G[N];
priority_queue<pair<long long, long long>, vector<pair<long long, long long> >,
               greater<pair<long long, long long> > >
    q;
long long dijkstra(int node, int lol, int he = 1) {
  for (int i = 0; i <= N - 1; ++i) dist[i] = INF;
  memset(vis, 0, sizeof(vis));
  memset(par, -1, sizeof(par));
  dist[node] = 0;
  q.push({dist[node], node});
  while (!q.empty()) {
    int u = q.top().second;
    q.pop();
    if (vis[u]) continue;
    vis[u] = 1;
    for (auto p : G[u]) {
      if (he == 0 && dis[u][p] == 0) continue;
      if (dist[p] > dist[u] + dis[u][p]) {
        par[p] = u;
        dist[p] = dist[u] + dis[u][p];
        q.push({dist[p], p});
      }
    }
  }
  return dist[lol];
}
set<pair<int, int> > E;
vector<pair<int, int> > EE;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int n, m, L, s, t;
  cin >> n >> m >> L >> s >> t;
  for (int i = 0; i <= m - 1; ++i) {
    int u, v, w;
    cin >> u >> v >> w;
    G[u].push_back(v);
    G[v].push_back(u);
    dis[u][v] = w;
    dis[v][u] = w;
    if (!w) E.insert({u, v});
    EE.push_back({u, v});
  }
  long long l = dijkstra(s, t, 0);
  if (l < L) {
    cout << "NO\n";
    return 0;
  }
  for (auto e : E) {
    dis[e.first][e.second] = dis[e.second][e.first] = 1;
  }
  l = dijkstra(s, t);
  if (l > L) {
    cout << "NO\n";
    return 0;
  }
  while (l < L) {
    int lol = t;
    set<pair<int, int> > hehe;
    while (lol != s) {
      int p = par[lol];
      hehe.insert({p, lol});
      hehe.insert({lol, p});
      lol = p;
    }
    for (auto it : E) {
      if (hehe.find(it) == hehe.end()) {
        dis[it.first][it.second] = INF;
        dis[it.second][it.first] = INF;
      }
    }
    for (auto it : E) {
      if (hehe.find(it) != hehe.end()) {
        dis[it.first][it.second] += (L - l);
        dis[it.second][it.first] += (L - l);
        break;
      }
    }
    l = dijkstra(s, t);
  }
  cout << "YES\n";
  for (auto e : EE) {
    cout << e.first << " " << e.second << " " << dis[e.first][e.second] << "\n";
  }
  return 0;
}
