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 long long inf = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1e9 + 7;
const int maxn = 2e4 + 10;
const int maxv = 1e3 + 10;
const double eps = 1e-9;
int n, m, s, t;
long long L;
int cnt, pnt[maxn], nxt[maxn], head[maxv], from[maxn];
long long cost[maxn];
bool can[maxn];
void add_edge(int u, int v, long long val) {
  from[cnt] = u;
  pnt[cnt] = v;
  cost[cnt] = val;
  nxt[cnt] = head[u];
  if (!cost[cnt]) can[cnt] = true;
  head[u] = cnt++;
}
void print() {
  for (int i = 0; i < cnt; i++) {
    cout << from[i] << ' ' << pnt[i] << ' ' << cost[i] << endl;
  }
}
void change(long long x) {
  for (int i = 0; i < cnt; i++) {
    if (can[i]) cost[i] = x;
  }
}
int vis[maxv];
long long dis[maxv];
int pedge[maxn];
long long dij() {
  memset(dis, 0x3f, sizeof dis);
  dis[s] = 0;
  memset(vis, 0, sizeof vis);
  priority_queue<pair<long long, long long>,
                 vector<pair<long long, long long> >,
                 greater<pair<long long, long long> > >
      pq;
  pq.push(pair<long long, long long>(0, s));
  while (pq.size()) {
    auto cur = pq.top();
    pq.pop();
    int u = cur.second;
    long long d = cur.first;
    vis[u] = 1;
    if (dis[u] < d) continue;
    for (int i = head[u]; ~i; i = nxt[i]) {
      int v = pnt[i];
      if (dis[v] > dis[u] + cost[i]) {
        dis[v] = dis[u] + cost[i];
        if (!vis[v]) pq.push(pair<long long, long long>(dis[v], v));
        pedge[v] = i ^ 1;
      }
    }
  }
  return dis[t];
}
int main() {
  cnt = 0;
  memset(head, -1, sizeof head);
  memset(can, 0, sizeof can);
  cin >> n >> m >> L >> s >> t;
  for (int i = 0; i < m; i++) {
    int u, v;
    long long val;
    cin >> u >> v >> val;
    add_edge(u, v, val);
    add_edge(v, u, val);
  }
  change(inf);
  if (dij() < L) {
    puts("NO");
    return 0;
  }
  change(1);
  if (dij() > L) {
    puts("NO");
    return 0;
  }
  int allss = 0;
  while (1) {
    long long now = dij();
    if (now >= L) break;
    for (int cur = t; cur != s; cur = pnt[pedge[cur]]) {
      int i = pedge[cur];
      if (can[i]) {
        cost[i] = cost[i ^ 1] += L - now;
        break;
      }
    }
  }
  puts("YES");
  for (int i = 0; i < cnt; i += 2) {
    printf("%d %d %lld\n", from[i], pnt[i], cost[i]);
  }
  return 0;
}
