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