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;
const int INF = 1e9;
const int N = 100031;
long long n, m, s, t, l;
long long a[N], b[N], w[N];
long long flag[N];
vector<int> g[N];
void run_locker(int val) {
  for (int i = 0; i < m; i++) {
    if (flag[i]) w[i] = val;
  }
}
int used[N];
long long dist[N];
int par[N];
int get_other(int edge_id, int v_id) {
  if (a[edge_id] == v_id) return b[edge_id];
  return a[edge_id];
}
long long get_solution() {
  for (int i = 1; i <= n; i++) {
    used[i] = 0;
    dist[i] = 1e18;
  }
  dist[s] = 0;
  set<pair<long long, long long> > S;
  set<pair<long long, long long> >::iterator it;
  for (int i = 1; i <= n; i++) {
    S.insert(make_pair(dist[i], i));
  }
  while (S.size()) {
    it = S.begin();
    pair<long long, long long> p = *it;
    S.erase(it);
    int qv = p.second;
    for (int i = 0; i < g[qv].size(); i++) {
      int id = g[qv][i];
      int to = get_other(id, qv);
      long long qd = dist[qv] + w[id];
      if (dist[to] > qd) {
        S.erase(make_pair(dist[to], to));
        dist[to] = qd;
        par[to] = id;
        S.insert(make_pair(dist[to], to));
      }
    }
  }
  return dist[t];
}
vector<int> get_path() {
  vector<int> res;
  int cur = t;
  while (cur != s) {
    res.push_back(par[cur]);
    cur = get_other(par[cur], cur);
  }
  return res;
}
vector<int> purify(vector<int> v) {
  vector<int> res;
  for (int i = 0; i < v.size(); i++) {
    int id = v[i];
    if (flag[id]) res.push_back(id);
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> m >> l >> s >> t;
  ++s;
  ++t;
  for (int i = 0; i < m; i++) {
    cin >> a[i] >> b[i] >> w[i];
    ++a[i];
    ++b[i];
    g[a[i]].push_back(i);
    g[b[i]].push_back(i);
    if (w[i] == 0) flag[i] = 1;
  }
  run_locker((int)1e9 + 1e6);
  long long Q = get_solution();
  if (Q < l) {
    cout << "NO" << endl;
    return 0;
  }
  run_locker(1);
  Q = get_solution();
  if (Q > l) {
    cout << "NO" << endl;
    return 0;
  }
  vector<int> V;
  for (int i = 0; i < m; i++) {
    if (flag[i]) V.push_back(i);
  }
  while (true) {
    long long Q = get_solution();
    if (Q == l) break;
    long long L, R;
    L = 0;
    R = 1e15;
    while (L < R) {
      long long mid = L + R + 1;
      mid /= 2;
      int C = V.size();
      for (int i = 0; i < V.size(); i++) {
        int id = V[i];
        w[id] += mid / C;
        if (i < mid % C) w[id]++;
      }
      long long QQ = get_solution();
      if (QQ > l) {
        R = mid - 1;
      } else {
        L = mid;
      }
      for (int i = 0; i < V.size(); i++) {
        int id = V[i];
        w[id] -= mid / C;
        if (i < mid % C) w[id]--;
      }
    }
    for (int i = 0; i < V.size(); i++) {
      int id = V[i];
      w[id] += L / V.size();
      if (i < L % V.size()) w[id]++;
    }
  }
  cout << "YES" << endl;
  for (int i = 0; i < m; i++) {
    --a[i];
    --b[i];
    cout << a[i] << " " << b[i] << " " << w[i] << endl;
  }
  cin.get();
  cin.get();
  return 0;
}
