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 max4 = 10004;
const int maxx = 200005;
const int max6 = 1000006;
const int lg5 = 17;
const int INF = 2 * 1000000007;
const long long INFLL = 4LL * 1000000000 * 1000000000;
int powmod(int a, int b, int mod) {
  int res = 1;
  a %= mod;
  for (; b; b >>= 1) {
    if (b & 1) {
      res = 1LL * res * a % mod;
    }
    a = 1LL * a * a % mod;
  }
  return res;
}
int gcd(int a, int b) {
  while (b > 0) {
    int t = a % b;
    a = b, b = t;
  }
  return a;
}
int lcm(int a, int b) { return (a / gcd(a, b)) * b; }
int is_prime(int n) {
  if (n <= 1 || n > 3 && (n % 2 == 0 || n % 3 == 0)) return 0;
  for (int i = 5, t = 2; i * i <= n; i += t, t = 6 - t)
    if (n % i == 0) return 0;
  return 1;
}
int n, m;
vector<pair<long long, int>> g[maxx];
int par[maxx];
long long Dijkstra(int st, int en) {
  vector<long long> dis(n + 1, INFLL);
  set<pair<long long, int>> s;
  s.insert({0, st});
  dis[st] = 0;
  while (!s.empty()) {
    auto cur = s.begin();
    s.erase(cur);
    int i = (*cur).second;
    long long w = (*cur).first;
    if (dis[i] < w) {
      continue;
    }
    for (auto v : g[i]) {
      if (dis[v.second] > dis[i] + v.first) {
        dis[v.second] = dis[i] + v.first;
        par[v.second] = i;
        s.insert({dis[v.second], v.second});
      }
    }
  }
  return dis[en];
}
int a[maxx], b[maxx];
long long c[maxx];
int main() {
  ios_base ::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  cin >> n >> m;
  int l, s, t;
  cin >> l >> s >> t;
  long long MX = 1e14;
  for (int i = 1; i <= m; i++) {
    cin >> a[i] >> b[i] >> c[i];
    if (c[i] == 0) c[i] = MX;
    g[a[i]].push_back({c[i], b[i]});
    g[b[i]].push_back({c[i], a[i]});
  }
  long long d = Dijkstra(s, t);
  if (d < l) {
    cout << "NO" << '\n';
    return 0;
  }
  for (int i = 1; i <= n; i++) g[i].clear();
  map<pair<int, int>, int> id;
  for (int i = 1; i <= m; i++) {
    if (c[i] == MX) {
      c[i] = 1;
      id[{a[i], b[i]}] = id[{b[i], a[i]}] = i;
    }
    g[a[i]].push_back({c[i], b[i]});
    g[b[i]].push_back({c[i], a[i]});
  }
  d = Dijkstra(s, t);
  if (d > l) {
    cout << "NO" << '\n';
    return 0;
  }
  if (d < l) {
    int cur = t;
    while (cur != s) {
      if (id.count({cur, par[cur]})) {
        c[id[{cur, par[cur]}]] += l - d;
        break;
      }
      cur = par[cur];
    }
  }
  cout << "YES" << '\n';
  for (int i = 1; i <= m; i++) {
    cout << a[i] << " " << b[i] << " " << c[i] << '\n';
  }
  return 0;
}
