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;
int n, m, L, s, t;
const long long LMAX = (long long)1e9;
const long long INF = (long long)1e15;
void nope() {
  cout << "NO" << '\n';
  exit(0);
}
struct ed {
  int u, v, w;
  int al;
} E[10100];
long long d[1010];
int p[1010], pe[1010];
vector<pair<int, int> > G[1010];
void djk(int s) {
  fill(d, d + n + 1, INF);
  fill(p, p + n + 1, -1);
  fill(pe, pe + n + 1, -1);
  set<pair<long long, int> > pq;
  d[s] = 0;
  pq.emplace(d[s], s);
  while (!pq.empty()) {
    int u = pq.begin()->second;
    pq.erase(pq.begin());
    long long du = d[u];
    for (auto& v : G[u]) {
      long long rlx = du + E[v.second].w;
      if (rlx < d[v.first]) {
        pq.erase({d[v.first], v.first});
        d[v.first] = rlx;
        p[v.first] = u;
        pe[v.first] = v.second;
        pq.emplace(d[v.first], v.first);
      }
    }
  }
}
void yep() {
  cout << "YES" << '\n';
  for (int e = 1; e <= m; e++) {
    cout << E[e].u << ' ' << E[e].v << ' ' << E[e].w << '\n';
  }
  exit(0);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  cin >> n >> m >> L >> s >> t;
  for (int u, v, w, e = 1; e <= m; e++) {
    cin >> u >> v >> w;
    E[e] = {u, v, w, w == 0};
    G[u].push_back({v, e});
    G[v].push_back({u, e});
  }
  for (int e = 1; e <= m; e++)
    if (E[e].al) E[e].w = 1;
  djk(s);
  if (p[t] == -1 or d[t] > L) nope();
  if (d[t] == L) yep();
  while (d[t] < L) {
    int diff = L - d[t];
    int v = t;
    bool inc = 0;
    for (; v >= 0; v = p[v])
      if (E[pe[v]].al) {
        E[pe[v]].w += diff;
        E[pe[v]].al = 0;
        inc = 1;
        break;
      }
    if (!inc) break;
    djk(s);
  }
  if (d[t] != L) nope();
  yep();
  return 0;
};
