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 d[1010][1010];
struct edge {
  int p1, p2, cost;
};
vector<edge> g;
vector<int> nvalue;
int n, m, s, t;
long long asked;
void calc() {
  for (int k = 0; k < n; k++)
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++) d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
  for (int i = 0; i < n; i++) d[i][i] = 0;
}
void printthem() {
  cout << "YES" << endl;
  for (int i = 0; i < g.size(); i++) {
    if (g[i].cost == 0)
      cout << g[i].p1 << " " << g[i].p2 << " "
           << "99999999\n";
    else
      cout << g[i].p1 << " " << g[i].p2 << " " << g[i].cost << endl;
  }
}
int main() {
  cin >> n >> m >> asked >> s >> t;
  int i, x, y, j;
  long long z;
  edge newedge;
  for (i = 0; i < n; i++)
    for (j = 0; j < n; j++) d[i][j] = 1000000000;
  for (i = 0; i < m; i++) {
    cin >> x >> y >> z;
    newedge.p1 = x;
    newedge.p2 = y;
    newedge.cost = z;
    g.push_back(newedge);
    if (z == 0) {
      nvalue.push_back(i);
    } else {
      d[x][y] = z;
      d[y][x] = z;
    }
  }
  calc();
  if (d[s][t] < asked) {
    cout << "NO" << endl;
    return 0;
  }
  int p1, p2, cost;
  for (i = 0; i < nvalue.size(); i++) {
    p1 = g[nvalue[i]].p1;
    p2 = g[nvalue[i]].p2;
    cost = g[nvalue[i]].cost;
    if (d[s][p1] < 1000000000 && d[p2][t] < 1000000000 &&
        asked - d[s][p1] - d[p2][t] >= 0) {
      g[nvalue[i]].cost = asked - d[s][p1] - d[p2][t];
      printthem();
      return 0;
    }
    p1 = g[nvalue[i]].p2;
    p2 = g[nvalue[i]].p1;
    if (d[s][p1] < 1000000000 && d[p2][t] < 1000000000 &&
        asked - d[s][p1] - d[p2][t] >= 0) {
      g[nvalue[i]].cost = asked - d[s][p1] - d[p2][t];
      printthem();
      return 0;
    }
  }
  cout << "NO" << endl;
}
