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 int MOD = 998244353;
const int N = 100005;
const double PI = 4 * atan(1);
const double eps = 1e-7;
const long long oo = 1e18;
const int AlPHA = 26, B = 30;
long long n, m, L, sr, t;
long long adj[1005][1005];
long long yes[1005][1005];
long long dist[1005];
vector<long long> ad[N];
bool vis[1005];
vector<pair<long long, long long> > v;
void dijkstra(long long src) {
  set<pair<long long, long long> > ss;
  pair<long long, long long> ras;
  for (int i = 0; i < n; i++) {
    dist[i] = 1e17;
    vis[i] = 0;
  }
  dist[src] = 0;
  ss.insert(make_pair(0, src));
  while (!ss.empty()) {
    ras = *(ss.begin());
    ss.erase(ss.begin());
    src = ras.second;
    long long w = ras.first;
    if (vis[src]) continue;
    vis[src] = 1;
    for (auto u : ad[src]) {
      if (dist[u] > w + adj[src][u]) {
        dist[u] = w + adj[src][u];
        ss.insert(make_pair(dist[u], u));
      }
    }
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin >> n >> m >> L >> sr >> t;
  for (int i = 0; i < m; i++) {
    long long x, y, z;
    cin >> x >> y >> z;
    ad[x].push_back(y);
    ad[y].push_back(x);
    if (z > 0) {
      adj[x][y] = adj[y][x] = z;
    } else {
      adj[x][y] = adj[y][x] = 1;
      yes[x][y] = yes[y][x] = 1;
      v.push_back(make_pair(x, y));
    }
  }
  dijkstra(sr);
  long long x = dist[t];
  long long i = 0;
  while (i < v.size() && x < L) {
    long long y = L - x + 1;
    adj[v[i].first][v[i].second] = adj[v[i].second][v[i].first] = y;
    dijkstra(sr);
    x = dist[t];
    i++;
  }
  if (x != L) {
    cout << "NO";
    return 0;
  } else {
    cout << "YES\n";
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        if (adj[i][j]) cout << i << " " << j << " " << adj[i][j] << "\n";
      }
    }
  }
  return 0;
}
