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 unsigned long long maxn = 1000 + 10;
const int INF = 0x3f3f3f3f;
const double eps = 1e-10;
const double pi = acos(-1.0);
int g[maxn][maxn];
struct haha {
  int x, y, w;
} p[maxn * 10], p0[maxn * 10];
struct Edge {
  int from, to, dist;
};
struct HeapNode {
  int d, u;
  bool operator<(const HeapNode& rhs) const { return d > rhs.d; }
};
struct Dijkstra {
  int n, m;
  vector<Edge> edges;
  vector<int> G[maxn];
  bool done[maxn];
  int d[maxn];
  int p[maxn];
  void init(int n) {
    this->n = n;
    for (int i = 0; i < n; ++i) G[i].clear();
    edges.clear();
  }
  void AddEdge(int from, int to, int dist) {
    edges.push_back((Edge){from, to, dist});
    m = edges.size();
    G[from].push_back(m - 1);
  }
  void dijkstra(int s) {
    priority_queue<HeapNode> Q;
    p[s] = -1;
    for (int i = 0; i < n; ++i) d[i] = INF;
    d[s] = 0;
    memset(done, 0, sizeof done);
    Q.push((HeapNode){0, s});
    while (!Q.empty()) {
      HeapNode x = Q.top();
      Q.pop();
      int u = x.u;
      if (done[u]) continue;
      done[u] = true;
      for (int i = 0; i < G[u].size(); ++i) {
        Edge& e = edges[G[u][i]];
        if (d[e.to] > d[u] + e.dist) {
          d[e.to] = d[u] + e.dist;
          p[e.to] = e.from;
          Q.push((HeapNode){d[e.to], e.to});
        }
      }
    }
  }
} dij;
int main() {
  int n, m, L, s, t;
  int cnt = 0, cnt2 = 0;
  scanf("%d %d %d %d %d", &n, &m, &L, &s, &t);
  dij.init(n);
  for (int i = 0; i < m; ++i) {
    int u, v, w;
    scanf("%d %d %d", &u, &v, &w);
    g[u][v] = g[v][u] = w;
    if (w) {
      p[cnt].x = u;
      p[cnt].w = w;
      p[cnt++].y = v;
      dij.AddEdge(u, v, w);
      dij.AddEdge(v, u, w);
    } else {
      p0[cnt2].x = u;
      p0[cnt2].w = 0;
      p0[cnt2++].y = v;
    }
  }
  dij.dijkstra(s);
  if (dij.d[t] < L) return 0 * puts("NO");
  if (dij.d[t] == L) {
    puts("YES");
    for (int i = 0; i < cnt; ++i) {
      printf("%d %d %d\n", p[i].x, p[i].y, p[i].w);
    }
    for (int i = 0; i < cnt2; ++i) {
      printf("%d %d %d\n", p0[i].x, p0[i].y, INF);
    }
    return 0;
  }
  int pos = -1;
  for (int i = 0; i < cnt2; ++i) {
    dij.AddEdge(p0[i].x, p0[i].y, 1);
    dij.AddEdge(p0[i].y, p0[i].x, 1);
    dij.dijkstra(s);
    if (dij.d[t] > L) continue;
    pos = i;
    break;
  }
  if (pos == -1) return 0 * puts("NO");
  puts("YES");
  for (int i = 0; i < cnt; ++i) {
    printf("%d %d %d\n", p[i].x, p[i].y, p[i].w);
  }
  for (int i = 0; i < pos; ++i) printf("%d %d %d\n", p0[i].x, p0[i].y, 1);
  printf("%d %d %d\n", p0[pos].x, p0[pos].y, L - dij.d[t] + 1);
  for (int i = pos + 1; i < cnt2; ++i)
    printf("%d %d %d\n", p0[i].x, p0[i].y, INF);
  return 0;
}
