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;
long long INF = 1e18;
struct edge {
  int to, cost;
  edge(int _to, int _cost) {
    to = _to;
    cost = _cost;
  };
};
vector<edge> G[1000];
int E[1000][1000];
int pre[1000];
long long d[1000];
long long n, m, L, s, t;
void init() { memset(pre, -1, sizeof(pre)); }
void dijkstra(int s) {
  fill(d, d + n, INF);
  priority_queue<pair<int, int>, vector<pair<int, int> >,
                 greater<pair<int, int> > >
      q;
  q.push(pair<int, int>(0, s));
  d[s] = 0;
  while (!q.empty()) {
    pair<int, int> p = q.top();
    q.pop();
    int v = p.second;
    if (d[v] < p.first) continue;
    for (int i = 0; i < G[v].size(); i++) {
      edge e = G[v][i];
      if (d[e.to] > d[v] + e.cost) {
        d[e.to] = d[v] + e.cost;
        pre[e.to] = v;
        q.push(pair<int, int>(d[e.to], e.to));
      }
    }
  }
}
bool flag = false;
int idx;
void dfs(int k) {
  if (flag) return;
  if (pre[k] != -1) {
    if (!E[pre[k]][k]) {
      E[pre[k]][k] = E[k][pre[k]] = L - d[t];
      flag = true;
      idx = k;
      return;
    }
    dfs(pre[k]);
  }
}
int main() {
  cin >> n >> m >> L >> s >> t;
  for (int i = 0; i < m; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    G[u].push_back(edge(v, w));
    G[v].push_back(edge(u, w));
    E[u][v] = E[v][u] = w;
  }
  init();
  dijkstra(s);
  if (d[t] > L) {
    cout << "NO" << endl;
  } else if (d[t] == L) {
    printf("YES\n");
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < G[i].size(); j++) {
        if (G[i][j].cost) {
          printf("%d %d %d\n", i, G[i][j].to, G[i][j].cost);
        } else {
          printf("%d %d %lld\n", i, G[i][j].to, INF);
        }
      }
    }
  } else {
    dfs(t);
    int tmp = t;
    if (!flag) {
      printf("NO\n");
    } else {
      printf("YES\n");
      bool vis[1000][1000];
      memset(vis, 0, sizeof(vis));
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < G[i].size(); j++) {
          if (!vis[i][G[i][j].to]) {
            if (E[i][G[i][j].to]) {
              printf("%d %d %d\n", i, G[i][j].to, E[i][G[i][j].to]);
            } else {
              printf("%d %d %lld\n", i, G[i][j].to, INF);
            }
            vis[i][G[i][j].to] = vis[G[i][j].to][i] = true;
          }
        }
      }
    }
  }
}
