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;
template <typename T>
void chmax(T& a, const T& b) {
  if (a < b) a = b;
}
template <typename T>
void chmin(T& a, const T& b) {
  if (a > b) a = b;
}
int N, M, L, S, T;
struct status {
  int prev, curr;
  long long total;
  bool operator>(const status& a) const { return total > a.total; }
};
struct edge {
  int to;
  long long cost;
};
list<edge> node[1000];
int back_track[1000];
const long long INF = 1e15;
long long dijkstra(long long erased) {
  priority_queue<status, vector<status>, greater<status> > pq;
  pq.push(status{-1, S, 0ll});
  memset(back_track, -1, sizeof(back_track));
  while (pq.empty() == false) {
    status st = pq.top();
    pq.pop();
    if (back_track[st.curr] != -1) continue;
    back_track[st.curr] = st.prev;
    if (st.curr == T) {
      return st.total;
    }
    for (auto&& it : node[st.curr]) {
      if (it.cost == 0ll) {
        pq.push(status{st.curr, it.to, st.total + erased});
      } else {
        pq.push(status{st.curr, it.to, st.total + it.cost});
      }
    }
  }
}
bool assign(int from, int to, long long cost) {
  for (auto&& it : node[from]) {
    if (it.to == to && it.cost == 0ll) {
      it.cost = cost;
      return true;
    }
  }
  return false;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> N >> M >> L >> S >> T;
  for (int i = (0); i < (M); i++) {
    int u, v;
    long long w;
    cin >> u >> v >> w;
    node[u].push_back(edge{v, w});
    node[v].push_back(edge{u, w});
  }
  long long total = dijkstra(INF);
  if (total < L) {
    cout << "NO" << endl;
    return 0;
  }
  total = dijkstra(1ll);
  if (total > L) {
    cout << "NO" << endl;
    return 0;
  }
  int curr = T;
  bool first = true;
  while (curr != S) {
    int prev = back_track[curr];
    if (first == false && assign(prev, curr, 1ll)) {
      assign(curr, prev, 1ll);
    } else if (first && assign(prev, curr, L - total + 1)) {
      assign(curr, prev, L - total + 1);
      first = false;
    }
    curr = prev;
  }
  cout << "YES" << endl;
  for (int i = (0); i < (N); i++) {
    for (auto&& it : node[i]) {
      if (it.to <= i) continue;
      if (it.cost == 0ll) it.cost = INF;
      cout << i << " " << it.to << " " << it.cost << endl;
    }
  }
  return 0;
}
