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 double eps = 1e-15;
const double pi = acos(-1.0);
const long long Mod = 1000000007;
const int N = 1e3 + 5;
int ks = 0;
int n, m, s, t;
long long dis[N], cost[N * 10], L;
int used[N], deleted[N * 10];
pair<int, int> parent[N];
vector<pair<int, int> > g[N];
struct edge {
  int x, y;
  long long z;
  bool operator<(const edge &f) const { return z > f.z; }
} E[N * 10];
void SPFA() {
  for (int i = 0; i < n; i++) {
    dis[i] = LLONG_MAX;
    used[i] = 0;
  }
  priority_queue<pair<long long, int>, vector<pair<long long, int> >,
                 greater<pair<long long, int> > >
      q;
  q.emplace(0, s);
  dis[s] = 0;
  while (q.size()) {
    int from = q.top().second;
    used[from] = 1;
    q.pop();
    for (auto i : g[from]) {
      int to = i.first;
      int id = i.second;
      if (dis[from] + cost[id] < dis[to]) {
        dis[to] = dis[from] + cost[id];
        parent[to] = {from, id};
        if (!used[to]) q.emplace(dis[to], to);
      }
    }
  }
}
int main() {
  scanf("%d%d%I64d%d%d", &n, &m, &L, &s, &t);
  for (int i = 0; i < m; i++) {
    scanf("%d%d%I64d", &E[i].x, &E[i].y, &E[i].z);
  }
  sort(E, E + m);
  int last = 0;
  for (int i = 0; i < m && E[i].z; i++, last++) {
    cost[i] = E[i].z;
    g[E[i].x].emplace_back(E[i].y, i);
    g[E[i].y].emplace_back(E[i].x, i);
  }
  SPFA();
  if (dis[t] < L) {
    puts("NO");
    return 0;
  }
  for (int i = last; i < m; i++) {
    deleted[i] = cost[i] = 1;
    g[E[i].x].emplace_back(E[i].y, i);
    g[E[i].y].emplace_back(E[i].x, i);
  }
  SPFA();
  if (dis[t] > L) {
    puts("NO");
    return 0;
  }
  puts("YES");
  while (dis[t] < L) {
    int cur = t;
    while (cur != s) {
      int id = parent[cur].second;
      cur = parent[cur].first;
      if (deleted[id]) {
        cost[id] += L - dis[t];
        break;
      }
    }
    SPFA();
  }
  bool done[N];
  memset(done, false, sizeof done);
  for (int i = 0; i < n; i++) {
    for (auto j : g[i]) {
      if (done[j.first]) continue;
      cout << i << ' ' << j.first << ' ' << cost[j.second] << '\n';
    }
    done[i] = true;
  }
}
