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;
vector<pair<long long int, int> > v[1005], as, test;
long long int n, m, l, s, t;
bool vis[1005];
bool zero[10050];
long long int value[10050];
long long int cost[1005];
int dij() {
  memset(vis, false, sizeof vis);
  for (int i = 0; i < n; i++) cost[i] = 1e18;
  multiset<pair<long long int, int> > q;
  q.insert({0, s});
  cost[s] = 0;
  while (!q.empty()) {
    pair<long long int, int> p = *q.begin();
    q.erase(q.begin());
    long long int y = p.first, x = p.second;
    if (vis[x]) continue;
    vis[x] = true;
    for (int i = 0; i < v[x].size(); i++) {
      if (cost[x] + value[v[x][i].second] < cost[v[x][i].first]) {
        cost[v[x][i].first] = cost[x] + value[v[x][i].second];
        q.insert({cost[v[x][i].first], v[x][i].first});
      }
    }
  }
  return cost[t];
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> n >> m >> l >> s >> t;
  long long int x, y, w;
  for (int i = 0; i < m; i++) {
    cin >> x >> y >> w;
    as.push_back(make_pair(x, y));
    v[x].push_back(make_pair(y, i));
    v[y].push_back(make_pair(x, i));
    if (!w) zero[i] = true;
    value[i] = w;
  }
  for (int i = 0; i < m; i++)
    if (zero[i]) value[i] = 1;
  long long int l_dis = dij();
  for (int i = 0; i < m; i++)
    if (zero[i]) value[i] = 2e9;
  long long int w_dis = dij();
  if (l_dis > l || !vis[t] || l > w_dis) {
    cout << "NO" << endl;
    return 0;
  }
  if (l_dis == w_dis) {
    cout << "YES" << endl;
    for (int i = 0; i < m; i++) {
      cout << as[i].first << " " << as[i].second << " " << value[i] << endl;
    }
    return 0;
  }
  for (int i = 0; i < m; i++) {
    if (zero[i]) {
      value[i] = 1;
      long long int val = dij();
      if (val <= l) {
        value[i] = 1 + (l - val);
        break;
      }
      if (val == w_dis) value[i] = 2e9;
    }
  }
  cout << "YES" << endl;
  for (int i = 0; i < m; i++) {
    cout << as[i].first << " " << as[i].second << " " << value[i] << endl;
  }
  return 0;
}
