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 n, m, L, s, t;
vector<pair<long long, long long> > adj[1111];
vector<long long> todo;
long long w[11111], u[11111], v[11111], d[1111];
void dijkstra() {
  for (long long i = 0; i <= n; i++) d[i] = (1LL << 60);
  d[s] = 0LL;
  priority_queue<pair<long long, long long> > pq;
  pq.push({0, s});
  while (!pq.empty()) {
    long long x = pq.top().second;
    long long t = -pq.top().first;
    pq.pop();
    if (d[x] < t) continue;
    for (auto i : adj[x]) {
      if (d[i.first] > d[x] + i.second) {
        d[i.first] = d[x] + i.second;
        pq.push({-d[i.first], i.first});
      }
    }
  }
}
long long check(long long x) {
  for (auto i : todo) {
    w[i] = 1 + min(x, 1000000000LL);
    x -= w[i] - 1;
  }
  for (long long i = 0; i <= n; i++) adj[i].clear();
  for (long long i = 0; i < m; i++) {
    adj[v[i]].push_back({u[i], w[i]});
    adj[u[i]].push_back({v[i], w[i]});
  }
  dijkstra();
  return d[t];
}
int main() {
  scanf("%lld%lld%lld%lld%lld", &n, &m, &L, &s, &t);
  for (long long i = 0; i < m; i++) {
    long long a, b, c;
    scanf("%lld%lld%lld", u + i, v + i, w + i);
    if (w[i] == 0) todo.push_back(i);
  }
  long long l = 0, d = 1000000000LL * todo.size(), mid, ans = -1;
  if (check(0) > L || check(d) < L) {
    printf("NO\n");
    return 0;
  }
  while (l <= d) {
    mid = (l + d) / 2;
    if (check(mid) <= L) {
      ans = mid;
      l = mid + 1;
    } else
      d = mid - 1;
  }
  check(ans);
  printf("YES\n");
  for (long long i = 0; i < m; i++) {
    printf("%lld %lld %lld\n", u[i], v[i], w[i]);
  }
  return 0;
}
