#include <bits/stdc++.h>
using namespace std;
const int N = 10011;
long long int n, m, s, t, l;
long long int dtf[N], dtb[N], dt[N];
vector<int> gr[N];
priority_queue<pair<long long int, long long int>,
               vector<pair<long long int, long long int> >,
               std::greater<pair<long long int, long long int> > >
    pq;
bool vs[N], is[N], ok;
int U[N], V[N], W[N];
int otherEnd(int u, int e) { return U[e] ^ V[e] ^ u; }
void dsp(long long int v) {
  while (!pq.empty()) pq.pop();
  for (long long int i = 0; i <= n + 4; ++i) vs[i] = 0, dt[i] = 1e17;
  dt[v] = 0;
  pq.push(make_pair(dt[v], v));
  while (!pq.empty()) {
    long long int pNode = (pq.top()).second;
    pq.pop();
    if (vs[pNode]) continue;
    vs[pNode] = 1;
    for (long long int i = 0; i < gr[pNode].size(); i++) {
      long long int curNode = otherEnd(pNode, gr[pNode][i]);
      long long int cost = W[gr[pNode][i]];
      if (cost == 0) cost = 1;
      if (dt[curNode] > dt[pNode] + cost) {
        dt[curNode] = dt[pNode] + cost;
        pq.push(make_pair(dt[curNode], curNode));
      }
    }
  }
}
void dsp2(long long int v) {
  while (!pq.empty()) pq.pop();
  for (long long int i = 0; i <= n + 4; ++i) vs[i] = 0, dt[i] = 1e17;
  dt[v] = 0;
  pq.push(make_pair(dt[v], v));
  while (!pq.empty()) {
    long long int pNode = (pq.top()).second;
    pq.pop();
    if (vs[pNode]) continue;
    vs[pNode] = 1;
    for (long long int i = 0; i < gr[pNode].size(); i++) {
      long long int curNode = otherEnd(pNode, gr[pNode][i]);
      long long int cost = W[gr[pNode][i]];
      if (cost == 0) {
        cost = max(1LL, l - (dt[pNode] + dtb[curNode]));
        W[gr[pNode][i]] = cost;
      }
      if (dt[curNode] > dt[pNode] + cost) {
        dt[curNode] = dt[pNode] + cost;
        pq.push(make_pair(dt[curNode], curNode));
      }
    }
  }
}
int main() {
  scanf("%lld", &n), scanf("%lld", &m), scanf("%lld", &l), scanf("%lld", &s),
      scanf("%lld", &t);
  s++, t++;
  for (int i = 0; i < m; ++i) {
    int u, v, w;
    scanf("%d", &u), scanf("%d", &v), scanf("%d", &w);
    u++, v++;
    is[i] = 1;
    U[i] = u, V[i] = v;
    W[i] = w;
    gr[u].push_back(i);
    gr[v].push_back(i);
  }
  dsp(t);
  for (int i = 1; i < n + 1; ++i) dtb[i] = dt[i];
  dsp2(s);
  if (dt[t] != l) {
    puts("NO");
    return 0;
  }
  puts("YES");
  for (int i = 0; i < m; ++i) {
    printf("%d %d %d\n", U[i] - 1, V[i] - 1, W[i]);
  }
  return 0;
}
