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;
int n;
bool vis[N];
int par[N];
vector<pair<long long, long long> > G[N];
long long dist[N];
priority_queue<pair<long long, long long>, vector<pair<long long, long long> >,
               greater<pair<long long, long long> > >
    q;
long long D[N][N];
long long dijkstra(int node, int out) {
  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 (dist[p.first] > dist[u] + D[u][p.first]) {
        dist[p.first] = dist[u] + D[u][p.first];
        par[p.first] = u;
        q.push({dist[p.first], p.first});
      }
    }
  }
  return dist[out];
}
vector<pair<long long, long long> > E;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int m, l, s, t;
  cin >> n >> m >> l >> s >> t;
  for (int i = 0; i <= m - 1; ++i) {
    int u, v;
    long long w;
    cin >> u >> v >> w;
    G[u].push_back({v, w});
    G[v].push_back({u, w});
    D[u][v] = w;
    D[v][u] = w;
    E.push_back({u, v});
  }
  int flag = 1;
  while (1) {
    long long lol = dijkstra(s, t);
    if (lol > l) {
      flag = 0;
      break;
    }
    if (lol == l) break;
    int g = 0;
    if (lol < l) {
      int f = t;
      while (f != s) {
        long long yo = D[par[f]][f];
        if (yo) {
          f = par[f];
          continue;
        }
        g = 1;
        D[par[f]][f] = l - lol;
        D[f][par[f]] = l - lol;
        break;
      }
    }
    if (!g) break;
  }
  if (flag == 1) {
    cout << "YES\n";
    for (auto it : E) {
      if (D[it.first][it.second] == 0) D[it.first][it.second] = INF;
      cout << it.first << " " << it.second << " " << D[it.first][it.second]
           << "\n";
    }
    return 0;
  }
  cout << "NO";
  return 0;
}
