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;
struct node {
  int a;
  long long d;
  node() {}
  node(int _a, long long _d) : a(_a), d(_d) {}
  bool operator<(const node &o) const { return d > o.d; }
};
struct edge {
  int a, b;
  long long d;
  edge() {}
  edge(int aa, int bb, int dd) : a(aa), b(bb), d(dd) {}
};
vector<node> table[1005];
vector<edge> tt, in;
long long ee[1005][1005];
long long dist[1005];
long long maxint = 2000000000;
bool spec[1005][1005];
int done[1005];
int from[1005];
int n, m;
priority_queue<node> Q;
void dijk1(int s) {
  while (!Q.empty()) Q.pop();
  for (int i = 0; i < n; i++) {
    dist[i] = maxint;
    done[i] = 0;
    from[i] = -1;
  }
  dist[s] = 0;
  from[s] = s;
  Q.push(node(s, 0));
  node tmp;
  int cnt = 0;
  int w, u;
  while (!Q.empty() && cnt < n) {
    if (done[Q.top().a] == 1) {
      Q.pop();
      continue;
    }
    tmp = Q.top();
    Q.pop();
    u = tmp.a;
    for (int i = 0; i < table[u].size(); i++) {
      w = table[u][i].a;
      if (dist[w] > dist[u] + ee[u][w]) {
        from[w] = u;
        dist[w] = dist[u] + ee[u][w];
        Q.push(node(w, dist[w]));
      }
    }
    done[u] = 1;
    cnt++;
  }
}
int main() {
  int L, s, t;
  scanf("%d%d%d%d%d", &n, &m, &L, &s, &t);
  int a, b, c;
  for (int i = 0; i < m; i++) {
    scanf("%d%d%d", &a, &b, &c);
    if (c == 0) {
      tt.push_back(edge(a, b, c));
      spec[a][b] = true;
      spec[b][a] = true;
      continue;
    }
    in.push_back(edge(a, b, c));
    ee[a][b] = c;
    ee[b][a] = c;
    table[a].push_back(node(b, c));
    table[b].push_back(node(a, c));
  }
  dijk1(s);
  if (dist[t] < L) {
    printf("NO");
    return 0;
  } else if (dist[t] == L) {
    printf("YES\n");
    for (int i = 0; i < in.size(); i++) {
      printf("%d %d %I64d \n", in[i].a, in[i].b, in[i].d);
    }
    for (int i = 0; i < tt.size(); i++) {
      printf("%d %d 1\n", tt[i].a, tt[i].b);
    }
  }
  for (int i = 0; i < tt.size(); i++) {
    a = tt[i].a;
    b = tt[i].b;
    ee[a][b] = 1;
    ee[b][a] = 1;
    table[a].push_back(node(b, 1));
    table[b].push_back(node(a, 1));
  }
  dijk1(s);
  if (dist[t] > L) {
    printf("NO");
    return 0;
  }
  for (int i = 0; i < tt.size(); i++) {
    a = tt[i].a;
    b = tt[i].b;
    ee[a][b] = L + 1;
    ee[b][a] = L + 1;
  }
  a = t;
  while (a != s) {
    b = from[a];
    if (spec[a][b]) {
      ee[a][b] = 1;
      ee[b][a] = 1;
    }
    a = b;
  }
  long long sum;
  while (dist[t] < L) {
    dijk1(s);
    if (dist[t] == L) break;
    a = t;
    while (a != s) {
      b = from[a];
      if (spec[a][b]) {
        ee[a][b] += L - dist[t];
        ee[b][a] += L - dist[t];
        break;
      }
      a = b;
    }
  }
  printf("YES\n");
  for (int i = 0; i < in.size(); i++) {
    printf("%d %d %I64d \n", in[i].a, in[i].b, in[i].d);
  }
  for (int i = 0; i < tt.size(); i++) {
    printf("%d %d %I64d \n", tt[i].a, tt[i].b, ee[tt[i].a][tt[i].b]);
  }
}
