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 = 0x3f3f3f3f;
const int maxn = 10000 + 16;
int head[maxn];
struct Edge {
  int v, w, next;
} edge[maxn * 2];
int cnt;
int n, m, L, s, t;
int inque[maxn];
int d[maxn];
int vis[maxn];
void add(int u, int v, int w) {
  edge[cnt].v = v;
  edge[cnt].w = w;
  edge[cnt].next = head[u];
  head[u] = cnt++;
}
void add_edge(int u, int v, int w) {
  add(u, v, w);
  add(v, u, w);
}
void init() {
  cnt = 0;
  memset(head, -1, sizeof(head));
  memset(inque, false, sizeof(inque));
  memset(d, INF, sizeof(d));
  memset(vis, 0, sizeof(vis));
}
void spfa(int s) {
  queue<int> Q;
  d[s] = 0;
  Q.push(s);
  inque[s] = true;
  while (!Q.empty()) {
    int u = Q.front();
    Q.pop();
    inque[u] = false;
    for (int i = head[u]; i != -1; i = edge[i].next) {
      int v = edge[i].v;
      int w = edge[i].w;
      if (d[v] > d[u] + w) {
        d[v] = d[u] + w;
        if (!inque[v]) {
          inque[v] = true;
          Q.push(v);
          if (vis[v] == n) {
            return;
          }
        }
      }
    }
  }
}
int u[maxn], v[maxn], w[maxn];
int main() {
  cin >> n >> m >> L >> s >> t;
  init();
  for (int i = 0; i < m; i++) {
    cin >> u[i] >> v[i] >> w[i];
    add_edge(u[i], v[i], w[i]);
  }
  spfa(s);
  if (d[t] >= L || d[t] == INF) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    for (int i = 0; i < m; i++) {
      cout << u[i] << " " << v[i] << " ";
      if (w[i] == 0)
        cout << L - d[t] << endl;
      else
        cout << w[i] << endl;
    }
  }
  return 0;
}
