#include <bits/stdc++.h>
using namespace std;
long long n, m, L, start, endP;
vector<vector<long long> > edges;
vector<vector<long long> > neighbors;
vector<vector<long long> > paths;
long long weights[1000][1000] = {0};
long long dijk() {
  vector<long long> distances(n, LLONG_MAX);
  distances[start] = 0;
  vector<bool> visited(n, false);
  priority_queue<pair<long long, long long>,
                 vector<pair<long long, long long> >,
                 greater<pair<long long, long long> > >
      pq;
  pq.push({0, start});
  while (!pq.empty()) {
    long long currentWeight = pq.top().first;
    long long currentNode = pq.top().second;
    pq.pop();
    if (visited[currentNode]) continue;
    visited[currentNode] = true;
    if (currentNode == endP) break;
    for (long long i = 0; i < neighbors[currentNode].size(); i++) {
      long long currNeighbor = neighbors[currentNode][i];
      long long currDist = weights[currentNode][currNeighbor];
      if (currDist == -1) continue;
      if (currentWeight + currDist < distances[currNeighbor])
        distances[currNeighbor] = currentWeight + currDist;
      if (!visited[currNeighbor])
        pq.push({distances[currNeighbor], currNeighbor});
    }
  }
  return distances[endP];
}
long long dijk2() {
  vector<long long> distances(n, LLONG_MAX);
  distances[start] = 0;
  vector<bool> visited(n, false);
  priority_queue<pair<long long, long long>,
                 vector<pair<long long, long long> >,
                 greater<pair<long long, long long> > >
      pq;
  pq.push({0, start});
  paths[start].push_back(start);
  while (!pq.empty()) {
    long long currentWeight = pq.top().first;
    long long currentNode = pq.top().second;
    pq.pop();
    if (visited[currentNode]) continue;
    visited[currentNode] = true;
    if (currentNode == endP) break;
    for (long long i = 0; i < neighbors[currentNode].size(); i++) {
      long long currNeighbor = neighbors[currentNode][i];
      long long currDist = weights[currentNode][currNeighbor];
      if (currDist == -1) currDist = 1;
      if (currentWeight + currDist < distances[currNeighbor]) {
        distances[currNeighbor] = currentWeight + currDist;
        paths[currNeighbor] = paths[currentNode];
        paths[currNeighbor].push_back(currNeighbor);
      }
      if (!visited[currNeighbor])
        pq.push({distances[currNeighbor], currNeighbor});
    }
  }
  return distances[endP];
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m >> L >> start >> endP;
  edges.resize(m);
  neighbors.resize(n);
  paths.resize(n);
  long long from, to, weight;
  for (long long i = 0; i < m; i++) {
    cin >> from >> to >> weight;
    if (weight == 0) weight = -1;
    weights[from][to] = weight;
    weights[to][from] = weight;
    edges[i] = {from, to, weight};
    neighbors[from].push_back(to);
    neighbors[to].push_back(from);
  }
  long long currMin = dijk();
  if (currMin < L) {
    cout << "NO" << endl;
    return 0;
  }
  long long newMin = dijk2();
  if (newMin > L) {
    cout << "NO" << endl;
    return 0;
  }
  for (long long i = 1; i < paths[endP].size(); i++) {
    long long prev = paths[endP][i - 1];
    long long curr = paths[endP][i];
    if (weights[prev][curr] == -1) {
      weights[prev][curr] = -2;
      weights[curr][prev] = -2;
    }
  }
  for (long long i = 0; i < edges.size(); i++) {
    long long from = edges[i][0];
    long long to = edges[i][1];
    long long weight = weights[from][to];
    if (weight == -1) {
      weights[from][to] = 999999999999;
      weights[to][from] = 999999999999;
    }
  }
  for (long long i = 1; i < paths[endP].size(); i++) {
    long long prev = paths[endP][i - 1];
    long long curr = paths[endP][i];
    if (weights[prev][curr] == -2) {
      weights[prev][curr] = -1;
      weights[curr][prev] = -1;
    }
  }
  while (newMin != L) {
    long long diff = L - newMin;
    for (long long i = 1; i < paths[endP].size(); i++) {
      long long prev = paths[endP][i - 1];
      long long curr = paths[endP][i];
      if (weights[prev][curr] == -1) {
        weights[prev][curr] = diff + 1;
        weights[curr][prev] = diff + 1;
        break;
      }
    }
    paths.clear();
    paths.resize(n);
    newMin = dijk2();
  }
  for (long long i = 1; i < paths[endP].size(); i++) {
    long long prev = paths[endP][i - 1];
    long long curr = paths[endP][i];
    if (weights[prev][curr] == -1) {
      weights[prev][curr] = 1;
      weights[curr][prev] = 1;
    }
  }
  cout << "YES" << endl;
  for (long long i = 0; i < edges.size(); i++) {
    long long from = edges[i][0];
    long long to = edges[i][1];
    long long weight = weights[from][to];
    if (weight == -1) weight = 999999999999;
    cout << from << ' ' << to << ' ' << weight << endl;
  }
  return 0;
}
