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;
int n, m, l, s, t;
vector<pair<pair<int, int>, int> > e;
vector<pair<int, int> > g[1005];
bool vis[1005];
int d[1005];
int dijkstra() {
  set<pair<int, int> > h;
  for (int i = 0; i < n; i++) {
    vis[i] = 0;
    d[i] = 0x3f3f3f3f;
  }
  d[s] = 0;
  h.insert(make_pair(d[s], s));
  while (!h.empty()) {
    int u = h.begin()->second;
    h.erase(h.begin());
    if (vis[u]) continue;
    if (u == t) return d[t];
    vis[u] = 1;
    for (int i = 0; i < g[u].size(); i++) {
      int v = g[u][i].first, w = g[u][i].second;
      if (d[u] + w <= l && d[u] + w < d[v]) {
        d[v] = d[u] + w;
        h.insert(make_pair(d[v], v));
      }
    }
  }
  return 0x3f3f3f3f;
}
int main() {
  scanf("%d %d %d %d %d", &n, &m, &l, &s, &t);
  for (int i = 0; i < m; i++) {
    int u, v, w;
    scanf("%d %d %d", &u, &v, &w);
    e.push_back(make_pair(make_pair(u, v), w));
    if (w > 0) {
      g[u].push_back(make_pair(v, w));
      g[v].push_back(make_pair(u, w));
    }
  }
  int x = dijkstra();
  if (x < l) {
    puts("NO");
    return 0;
  }
  if (x == l) {
    puts("YES");
    for (int i = 0; i < e.size(); i++) {
      if (e[i].second == 0) e[i].second = l + 1;
      printf("%d %d %d\n", e[i].first.first, e[i].first.second, e[i].second);
    }
    return 0;
  }
  for (int i = 0; i < e.size(); i++) {
    if (e[i].second > 0) continue;
    int u = e[i].first.first, v = e[i].first.second;
    g[u].push_back(make_pair(v, 1));
    g[v].push_back(make_pair(u, 1));
    int x = dijkstra();
    if (x > l) continue;
    e[i].second = l - x + 1;
    g[u][g[u].size() - 1].second = e[i].second;
    g[v][g[v].size() - 1].second = e[i].second;
    break;
  }
  if (dijkstra() != l) {
    puts("NO");
    return 0;
  }
  puts("YES");
  for (int i = 0; i < e.size(); i++) {
    if (e[i].second == 0) e[i].second = l + 1;
    printf("%d %d %d\n", e[i].first.first, e[i].first.second, e[i].second);
  }
}
