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;
long long mat[N][N];
bool road[N][N];
int n, m, L, s, t;
long long dist[N];
int par[N];
struct edge {
  int x, y;
  long long r;
  edge() {}
  edge(int _x, int _y, int _r) : x(_x), y(_y), r(_r) {}
} e[N];
vector<int> adj[N];
int djikstra() {
  for (int i = 0; i < n; i++) {
    dist[i] = inf;
    par[i] = -1;
  }
  dist[s] = 0;
  priority_queue<pair<long long, int> > pq;
  pq.push(make_pair(0, s));
  while (!pq.empty()) {
    long long w = -pq.top().first;
    int u = pq.top().second;
    pq.pop();
    if (dist[u] < w) continue;
    for (int i = 0; i < adj[u].size(); i++) {
      int v = adj[u][i];
      if (dist[u] + mat[u][v] < dist[v] && road[u][v]) {
        par[v] = u;
        dist[v] = dist[u] + mat[u][v];
        pq.push(make_pair(-dist[v], v));
      }
    }
  }
}
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++) {
      road[i][j] = 0;
    }
  }
  for (int i = 0; i < m; i++) {
    int x, y;
    long long r;
    cin >> x >> y >> r;
    road[x][y] = 1;
    road[y][x] = 1;
    mat[x][y] = r;
    mat[y][x] = r;
    adj[x].push_back(y);
    adj[y].push_back(x);
    e[i] = edge(x, y, r);
  }
  bool f = 0;
  while (1) {
    djikstra();
    if (dist[t] == inf) break;
    int cur = t;
    int cnt = 0;
    while (par[cur] != -1) {
      cnt += (mat[par[cur]][cur] == 0);
      cur = par[cur];
    }
    if (dist[t] + cnt <= L) {
      int gv = L - dist[t];
      cur = t;
      while (par[cur] != -1) {
        if (mat[par[cur]][cur] == 0) {
          mat[par[cur]][cur] = (gv - cnt + 1);
          mat[cur][par[cur]] = (gv - cnt + 1);
          cnt--;
          gv = cnt;
        }
        road[par[cur]][cur] = 0;
        road[cur][par[cur]] = 0;
        cur = par[cur];
      }
      f = 1;
    } else {
      cur = t;
      while (par[cur] != -1) {
        road[par[cur]][cur] = 0;
        road[cur][par[cur]] = 0;
        cur = par[cur];
      }
    }
  }
  if (!f) {
    cout << "NO"
         << "\n";
  } else {
    cout << "YES"
         << "\n";
    for (int i = 0; i < m; i++) {
      int t = mat[e[i].x][e[i].y];
      cout << e[i].x << " " << e[i].y << " " << ((t == 0) ? inf : t) << "\n";
    }
  }
  return 0;
}
