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 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;
}
