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;
queue<long long> q;
typedef struct edge {
  long long next, to, era;
  long long length;
};
typedef struct point {
  long long first, pre1, pre2;
  long long dis;
};
edge edg[2 * 10010];
point poi[10010];
long long e = 0;
void addedge(long long u, long long v, long long length) {
  edg[e].to = v;
  edg[e].length = length;
  edg[e].next = poi[u].first;
  poi[u].first = e++;
  edg[e].to = u;
  edg[e].length = length;
  edg[e].next = poi[v].first;
  poi[v].first = e++;
  if (!length) {
    edg[e - 1].era = true;
    edg[e - 2].era = true;
  } else {
    edg[e + 1].era = false;
    edg[e - 2].era = false;
  }
}
void bfs() {
  long long i, j;
  while (!q.empty()) {
    for (i = q.front(), q.pop(), j = poi[i].first; j != -1; j = edg[j].next)
      if (poi[edg[j].to].dis > poi[i].dis + edg[j].length) {
        q.push(edg[j].to);
        poi[edg[j].to].dis = poi[i].dis + edg[j].length;
        poi[edg[j].to].pre1 = i;
        poi[edg[j].to].pre2 = j;
      }
  }
}
int main() {
  long long n, m, s, t, i, u, v, L, length;
  scanf("%I64d%I64d%I64d%I64d%I64d", &n, &m, &L, &s, &t);
  for (i = 0; i < n; i++) poi[i].first = -1;
  for (i = 0; i < m; i++) {
    scanf("%I64d%I64d%I64d", &u, &v, &length);
    addedge(u, v, length);
  }
  for (i = 0; i < 2 * m; i++)
    if (edg[i].era) edg[i].length = 1000000000000000000;
  for (i = 0; i < n; i++) {
    q.push(i);
    poi[i].dis = 1000000000000000000;
  }
  poi[s].dis = 0;
  bfs();
  if (poi[t].dis < L) {
    printf("NO\n");
    return 0;
  }
  if (poi[t].dis == L) {
    printf("YES\n");
    for (i = 0; i < m; i++)
      printf("%I64d %I64d %I64d\n", edg[2 * i + 1].to, edg[2 * i].to,
             edg[2 * i].length);
    return 0;
  }
  for (i = 0; i < 2 * m; i++)
    if (edg[i].era) edg[i].length = 1;
  for (i = 0; i < n; i++) {
    q.push(i);
    poi[i].dis = 1000000000000000000;
  }
  poi[s].dis = 0;
  poi[s].pre1 = -1;
  poi[s].pre2 = -1;
  bfs();
  if (poi[t].dis > L) {
    printf("NO\n");
    return 0;
  }
  if (poi[t].dis < L) {
    for (i = 0; i < 2 * m; i++)
      if (edg[i].era) edg[i].length = 1000000000000000000;
    i = t;
    while (!edg[poi[i].pre2].era) i = poi[i].pre1;
    edg[poi[i].pre2].length = 1 + L - poi[t].dis;
    edg[poi[i].pre2 ^ 1].length = 1 + L - poi[t].dis;
    while (poi[i].pre1 != -1) {
      i = poi[i].pre1;
      if (edg[poi[i].pre2].era) {
        edg[poi[i].pre2].length = 1;
        edg[poi[i].pre2 ^ 1].length = 1;
      }
    }
  }
  printf("YES\n");
  for (i = 0; i < m; i++)
    printf("%I64d %I64d %I64d\n", edg[2 * i + 1].to, edg[2 * i].to,
           edg[2 * i].length);
  return 0;
}
