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;
struct Edge {
  int from, to, weight;
  Edge(int u = 0, int v = 0, int w = 0) : from(u), to(v), weight(w) {}
};
struct Node {
  int x, dis, par;
  Node(int n = 0, int d = 0, int p = -1) : x(n), dis(d), par(p) {}
  bool operator>(const Node &n) const { return dis > n.dis; }
};
int n, m, L, s, t, u, v, w;
Edge edges[22000];
vector<int> g[1200];
int dis[1200], vis[1200], par[1200];
void output() {
  printf("YES\n");
  for (int i = 0; i < m; ++i) {
    if (edges[2 * i].weight == 0)
      printf("%d %d 1000000000000000\n", edges[2 * i].from, edges[2 * i].to);
    else
      printf("%d %d %d\n", edges[2 * i].from, edges[2 * i].to,
             edges[2 * i].weight);
  }
}
int main() {
  scanf("%d%d%d%d%d", &n, &m, &L, &s, &t);
  for (int i = 0; i < m; ++i) {
    scanf("%d%d%d", &u, &v, &w);
    edges[2 * i] = Edge(u, v, w);
    edges[2 * i + 1] = Edge(v, u, w);
    g[u].push_back(2 * i);
    g[v].push_back(2 * i + 1);
  }
  priority_queue<Node, vector<Node>, greater<Node> > q;
  memset(vis, 0, sizeof(vis));
  q.push(Node(s, 0));
  for (int i = 0; i < n; ++i) dis[i] = 1e9 + 7;
  dis[s] = 0;
  while (!q.empty()) {
    Node u = q.top();
    int x = u.x;
    q.pop();
    if (vis[x]) continue;
    vis[x] = 1;
    for (int i = 0; i < g[x].size(); ++i) {
      Edge &e = edges[g[x][i]];
      if (e.weight > 0 && !vis[e.to] && dis[e.to] > dis[x] + e.weight) {
        dis[e.to] = dis[x] + e.weight;
        q.push(Node(e.to, dis[e.to]));
      }
    }
  }
  if (dis[t] < L)
    printf("NO\n");
  else if (dis[t] == L)
    output();
  else {
    memset(vis, 0, sizeof(vis));
    q.push(Node(s, 0));
    for (int i = 0; i < n; ++i) dis[i] = 1e9 + 7;
    dis[s] = 0;
    while (!q.empty()) {
      Node u = q.top();
      int x = u.x;
      q.pop();
      if (vis[x]) continue;
      vis[x] = 1;
      par[x] = u.par;
      for (int i = 0; i < g[x].size(); ++i) {
        Edge &e = edges[g[x][i]];
        if (!vis[e.to] && dis[e.to] > dis[x] + e.weight) {
          dis[e.to] = dis[x] + e.weight;
          q.push(Node(e.to, dis[e.to], g[x][i]));
        }
      }
    }
    if (dis[t] == 1e9 + 7 || dis[t] >= L)
      printf("NO\n");
    else {
      int cnt = 0;
      for (int u = t; u != s; u = edges[par[u]].from)
        if (edges[par[u]].weight == 0) ++cnt;
      if (cnt > L - dis[t])
        printf("NO\n");
      else {
        int j = 0, remain = L - dis[t];
        for (int u = t; u != s; u = edges[par[u]].from) {
          if (edges[par[u]].weight == 0) {
            ++j;
            if (j == cnt)
              edges[par[u]].weight = remain;
            else {
              edges[par[u]].weight = 1;
              remain--;
            }
          }
        }
      }
      output();
    }
  }
  return 0;
}
