#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1000;
const long long INF = 1e18;
vector<pair<int, int> > v[MAXN + 1];
priority_queue<pair<long long, int> > q;
long long dist[MAXN + 1];
int cnt = 0;
long long* ret;
long long value[10001];
bool ck[1001][1001];
bool change;
void djik(int s, int e, int I) {
  change = false;
  for (int i = 0; i < 1001; i++) dist[i] = INF;
  dist[s] = 0;
  q.push(make_pair(0LL, s));
  while (!q.empty()) {
    long long cost = -q.top().first;
    int x = q.top().second;
    q.pop();
    if (cost > dist[x]) continue;
    for (int i = 0; i < v[x].size(); i++) {
      if (value[v[x][i].second] >= INF && cnt < I) {
        ret = &value[v[x][i].second];
        *ret = 1;
        cnt++;
        change = true;
      }
      long long weight = cost + value[v[x][i].second];
      int next = v[x][i].first;
      if (dist[next] > weight) {
        dist[next] = weight;
        q.push(make_pair(-weight, next));
      }
    }
  }
}
int main() {
  int n, m, L, s, e;
  int zerocnt = 0;
  scanf("%d %d %d %d %d", &n, &m, &L, &s, &e);
  for (int i = 0; i < m; i++) {
    int a, b;
    long long w;
    scanf("%d %d %lld", &a, &b, &w);
    if (w == 0) {
      w = 1e18;
      zerocnt++;
    }
    value[i] = w;
    v[a].push_back(make_pair(b, i));
    v[b].push_back(make_pair(a, i));
  }
  djik(s, e, 0);
  if (dist[e] < L) {
    printf("NO");
    return 0;
  } else if (dist[e] == L) {
    printf("YES\n");
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < v[j].size(); k++) {
        if (!ck[j][v[j][k].first])
          printf("%d %d %lld\n", j, v[j][k].first, value[v[j][k].second]);
        ck[j][v[j][k].first] = ck[v[j][k].first][j] = true;
      }
    }
    return 0;
  }
  for (int i = 1; i <= zerocnt; i++) {
    djik(s, e, i);
    if (dist[e] <= L) {
      printf("YES\n");
      if (change) *ret += L - dist[e];
      for (int j = 0; j < n; j++) {
        for (int k = 0; k < v[j].size(); k++) {
          if (!ck[j][v[j][k].first])
            printf("%d %d %lld\n", j, v[j][k].first, value[v[j][k].second]);
          ck[j][v[j][k].first] = ck[v[j][k].first][j] = true;
        }
      }
      return 0;
    }
  }
  printf("NO");
}
