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 int n, m, l, s, t, a, b, weight, inf = 2e18;
vector<vector<long long int>> adj1(1005), adj2(1005);
vector<long long int> d(1005), p(1005);
long long int fixedd[1005][1005], variable[1005][1005];
void dijkstra(vector<long long int> &d, vector<long long int> &p) {
  d.assign(n + 1, inf);
  p.assign(n + 1, -1);
  set<pair<long long int, long long int>> S;
  S.insert({0, s});
  d[s] = 0;
  while (!S.empty()) {
    pair<long long int, long long int> x = *S.begin();
    S.erase(S.begin());
    for (int y : adj1[x.second]) {
      if (d[x.second] + fixedd[x.second][y] < d[y]) {
        S.erase({d[y], y});
        d[y] = d[x.second] + fixedd[x.second][y];
        S.insert({d[y], y});
        p[y] = x.second;
      }
    }
  }
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m >> l >> s >> t;
  memset(fixedd, 0, sizeof(fixedd));
  memset(variable, 0, sizeof(variable));
  for (long long int i = 0; i < m; i++) {
    cin >> a >> b >> weight;
    if (weight == 0) {
      adj2[a].push_back(b);
      adj2[b].push_back(a);
      variable[a][b] = 1;
      variable[b][a] = 1;
    } else {
      adj1[a].push_back(b);
      adj1[b].push_back(a);
      fixedd[a][b] = weight;
      fixedd[b][a] = weight;
    }
  }
  dijkstra(d, p);
  if (d[t] < l) {
    cout << "NO\n";
    return 0;
  }
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < adj2[i].size(); j++) {
      adj1[i].push_back(adj2[i][j]);
      fixedd[i][adj2[i][j]] = 1;
    }
  }
  dijkstra(d, p);
  if (d[t] > l) {
    cout << "NO\n";
    return 0;
  }
  cout << "YES\n";
  while (d[t] != l) {
    long long int x = t;
    while (p[x] != -1) {
      if (variable[x][p[x]]) {
        fixedd[x][p[x]] += l - d[t];
        fixedd[p[x]][x] += l - d[t];
        break;
      } else
        x = p[x];
    }
    dijkstra(d, p);
  }
  long long int done[1005][1005];
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < n; j++) {
      if (done[i][j] == 0 && done[j][i] == 0 && fixedd[i][j] != 0) {
        cout << i << " " << j << " " << fixedd[i][j] << '\n';
        done[i][j] = 1;
      }
    }
  }
  return 0;
}
