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;
void init_ios() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
}
const int N = 1010;
const int INF = (int)1e9 + 10;
int n, m, l, s, t, d[N], dis[N][N];
vector<int> child[N];
vector<pair<pair<int, int>, int>> ed;
vector<int> zle;
void dijkstra(bool flag) {
  for (int i = 0; i < n; ++i) d[i] = INF;
  d[s] = 0;
  set<pair<int, int>> se;
  se.insert({d[s], s});
  while (!se.empty()) {
    auto it = *se.begin();
    se.erase(se.begin());
    for (auto dz : child[it.second]) {
      if (flag && dis[it.second][dz] == 0) continue;
      if (d[dz] > it.first + dis[it.second][dz]) {
        se.erase({d[dz], dz});
        d[dz] = it.first + dis[it.second][dz];
        se.insert({d[dz], dz});
      }
    }
  }
}
int main() {
  init_ios();
  cin >> n >> m >> l >> s >> t;
  for (int i = 0; i < m; ++i) {
    int x, y, z;
    cin >> x >> y >> z;
    dis[x][y] = dis[y][x] = z;
    ed.push_back({{x, y}, z});
    child[x].push_back(y);
    child[y].push_back(x);
    if (z == 0) zle.push_back(i);
  }
  dijkstra(true);
  if (d[t] < l) {
    cout << "NO\n";
    return 0;
  }
  int x1 = 1, x2 = INF - 5, x3;
  while (x2 - x1 > 1) {
    x3 = (x1 + x2) / 2;
    for (auto i : zle) {
      int u = ed[i].first.first, v = ed[i].first.second;
      dis[u][v] = dis[v][u] = x3;
    }
    dijkstra(false);
    if (d[t] > l)
      x2 = x3;
    else
      x1 = x3;
  }
  for (auto i : zle) {
    int u = ed[i].first.first, v = ed[i].first.second;
    dis[u][v] = dis[v][u] = x1;
  }
  dijkstra(false);
  if (d[t] > l) {
    cout << "NO\n";
    return 0;
  }
  if (d[t] == l) {
    cout << "YES\n";
    for (auto it : ed)
      cout << it.first.first << " " << it.first.second << " "
           << dis[it.first.first][it.first.second] << "\n";
    return 0;
  }
  for (auto i : zle) {
    int u = ed[i].first.first, v = ed[i].first.second;
    dis[u][v] = dis[v][u] = x1 + 1;
    dijkstra(false);
    if (d[t] == l) {
      cout << "YES\n";
      for (auto it : ed)
        cout << it.first.first << " " << it.first.second << " "
             << dis[it.first.first][it.first.second] << "\n";
      return 0;
    }
  }
  cout << "NO\n";
}
