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 MAXN = 1000;
const long long IINF = 10e17;
vector<pair<int, int> > e[MAXN];
vector<pair<int, int> > ept;
vector<pair<pair<int, int>, int> > nept;
queue<int> que;
bool inq[MAXN];
long long d[MAXN];
int n, m, target, st, ed;
void spfa() {
  for (int i = 0; i < n; i++) {
    d[i] = i == st ? 0 : IINF;
    inq[i] = i == st ? true : false;
  }
  que.push(st);
  while (!que.empty()) {
    int u = que.front();
    que.pop();
    inq[u] = false;
    for (int i = 0; i < e[u].size(); i++) {
      int v = e[u][i].first;
      int w = e[u][i].second;
      if (d[u] + w < d[v]) {
        d[v] = d[u] + w;
        if (!inq[v]) {
          que.push(v);
          inq[v] = true;
        }
      }
    }
  }
}
int main() {
  while (scanf("%d%d%d%d%d", &n, &m, &target, &st, &ed) != EOF) {
    for (int i = 0; i < n; i++) e[i].clear();
    ept.clear();
    nept.clear();
    for (int i = 0; i < m; i++) {
      int u, v, w;
      scanf("%d%d%d", &u, &v, &w);
      if (w) {
        e[u].push_back(make_pair(v, w));
        e[v].push_back(make_pair(u, w));
        nept.push_back(make_pair(make_pair(u, v), w));
      } else {
        ept.push_back(make_pair(u, v));
      }
    }
    spfa();
    if (d[ed] < target) {
      puts("NO");
      continue;
    } else if (d[ed] == target) {
      puts("YES");
      for (int i = 0; i < nept.size(); i++) {
        printf("%d %d %d\n", nept[i].first.first, nept[i].first.second,
               nept[i].second);
      }
      for (int i = 0; i < ept.size(); i++) {
        cout << ept[i].first << " " << ept[i].second << " " << IINF << endl;
      }
      continue;
    }
    int index = -1, weight = 0;
    for (int i = 0; i < ept.size(); i++) {
      int u = ept[i].first;
      int v = ept[i].second;
      e[u].push_back(make_pair(v, 1));
      e[v].push_back(make_pair(u, 1));
      spfa();
      if (d[ed] <= target) {
        index = i;
        weight = 1 + target - d[ed];
        continue;
      }
    }
    if (index == -1) {
      puts("NO");
    } else {
      puts("YES");
      for (int i = 0; i < nept.size(); i++) {
        printf("%d %d %d\n", nept[i].first.first, nept[i].first.second,
               nept[i].second);
      }
      for (int i = 0; i < index; i++) {
        printf("%d %d %d\n", ept[i].first, ept[i].second, 1);
      }
      cout << ept[index].first << " " << ept[index].second << " " << weight
           << endl;
      for (int i = index + 1; i < ept.size(); i++) {
        cout << ept[i].first << " " << ept[i].second << " " << IINF << endl;
      }
    }
  }
  return 0;
}
