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 = 1LL * 1e18;
const int N = 1010;
const int M = 10010;
struct edge {
  int x, y;
  long long r;
} e[M];
long long mat[N][N];
int n, m, s, t;
long long L;
long long dist[N];
long long lvl[N];
int par[N];
void djikstra(bool b) {
  for (int i = 0; i < n; i++) {
    dist[i] = lvl[i] = inf;
    par[i] = -1;
  }
  dist[s] = lvl[s] = 0;
  priority_queue<pair<pair<long long, int>, int>,
                 vector<pair<pair<long long, int>, int> >,
                 greater<pair<pair<long long, int>, int> > >
      pq;
  pq.push(make_pair(make_pair(0, 0), s));
  while (!pq.empty()) {
    long long w = pq.top().first.first;
    int l = pq.top().first.second;
    int u = pq.top().second;
    pq.pop();
    for (int i = 0; i < n; i++) {
      if (b && mat[u][i] == 0) continue;
      if (w + mat[u][i] < dist[i] ||
          (w + mat[u][i] == dist[i] && l + 1 < lvl[i])) {
        lvl[i] = l + 1;
        dist[i] = w + mat[u][i];
        par[i] = u;
        pq.push(make_pair(make_pair(dist[i], lvl[i]), i));
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> m >> L >> s >> t;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      mat[i][j] = inf;
    }
  }
  for (int i = 0; i < m; i++) {
    cin >> e[i].x >> e[i].y >> e[i].r;
    mat[e[i].x][e[i].y] = e[i].r;
    mat[e[i].y][e[i].x] = e[i].r;
  }
  djikstra(1);
  if (dist[t] < L) {
    cout << "NO"
         << "\n";
    return 0;
  }
  if (dist[t] == L) {
    cout << "YES"
         << "\n";
    for (int i = 0; i < m; i++) {
      int val = mat[e[i].x][e[i].y];
      cout << e[i].x << " " << e[i].y << " " << (val == 0 ? inf : val) << "\n";
    }
    return 0;
  }
  djikstra(0);
  int ce = 0;
  int v = t;
  while (par[v] != -1) {
    int u = par[v];
    ce += !mat[u][v];
    v = par[v];
  }
  if (ce + dist[t] > L) {
    cout << "NO"
         << "\n";
    return 0;
  }
  v = t;
  int gv = L - dist[t];
  while (par[v] != -1) {
    int u = par[v];
    if (!mat[u][v]) {
      mat[u][v] = (gv - ce + 1);
      ce = gv = ce - 1;
    }
    v = u;
  }
  cout << "YES"
       << "\n";
  for (int i = 0; i < m; i++) {
    int val = mat[e[i].x][e[i].y];
    cout << e[i].x << " " << e[i].y << " " << (val == 0 ? inf : val) << "\n";
  }
  return 0;
}
