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, l, s, t, u, v, w;
long long ste[1010];
long long sts[1010];
vector<pair<long long, long long> > pa[1010];
void opa() {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < pa[i].size(); j++) {
      if (i < pa[i][j].second) {
        cout << i << ' ' << pa[i][j].second << ' ';
        cout << (pa[i][j].first > 0 ? pa[i][j].first : 10000000000000000)
             << '\n';
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m >> l >> s >> t;
  for (int i = 0; i < m; i++) {
    cin >> u >> v >> w;
    pa[u].push_back({w, v});
    pa[v].push_back({w, u});
  }
  memset(ste, -1, sizeof ste);
  memset(sts, -1, sizeof sts);
  priority_queue<pair<long long, long long> > pq;
  while (!pq.empty()) pq.pop();
  pq.push({0, t});
  while (!pq.empty()) {
    long long now = pq.top().second;
    long long np = pq.top().first;
    pq.pop();
    if (ste[now] != -1) continue;
    ste[now] = np;
    for (int i = 0; i < pa[now].size(); i++) {
      if (ste[pa[now][i].second] == -1 && pa[now][i].first != 0) {
        pq.push({np + pa[now][i].first, pa[now][i].second});
      }
    }
  }
  if (ste[s] != -1) {
    if (ste[s] < l) cout << "NO\n";
    return 0;
  }
  while (!pq.empty()) pq.pop();
  pq.push({0, s});
  bool done = 0;
  while (!pq.empty()) {
    long long now = pq.top().second;
    long long np = pq.top().first;
    pq.pop();
    if (sts[now] != -1) continue;
    sts[now] = np;
    for (int i = 0; i < pa[now].size(); i++) {
      int nex = pa[now][i].second;
      if (sts[nex] == -1) {
        if (pa[now][i].first != 0)
          pq.push({np + pa[now][i].first, nex});
        else {
          if (ste[nex] != -1) {
            if (sts[now] + ste[nex] < l) {
              pa[now][i].first = l - sts[now] - ste[nex];
              done = 1;
              break;
            } else {
              pa[now][i].first = 1;
              pq.push({np + pa[now][i].first, nex});
            }
          }
        }
      }
    }
    if (done) {
      break;
    }
  }
  if (done || ste[s] == l) {
    cout << "YES\n";
    opa();
  } else
    cout << "NO\n";
}
