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 edge {
  int to, next, v, mk;
} e[20010 << 2];
int head[20010];
int cnt;
int n, m, l, s, E;
int t, h;
int dis[20010], vis[20010], q[20010];
void link(int x, int y, int z, int w) {
  e[cnt] = (edge){y, head[x], z, w};
  head[x] = cnt++;
}
void add(int x, int y, int z, int w) {
  link(x, y, z, w);
  link(y, x, z, w);
}
void SPFA() {
  memset(vis, 0, sizeof(vis));
  memset(dis, 63, sizeof(dis));
  h = 0;
  q[t = 1] = s;
  vis[s] = 1;
  dis[s] = 0;
  while (h != t) {
    int now = q[h = h % n + 1];
    vis[now] = 0;
    for (int i = head[now]; ~i; i = e[i].next) {
      int y = e[i].to;
      if (dis[y] > dis[now] + e[i].v) {
        dis[y] = dis[now] + e[i].v;
        if (!vis[y]) {
          vis[y] = 1;
          q[t = t % n + 1] = y;
        }
      }
    }
  }
}
int main() {
  memset(head, -1, sizeof(head));
  scanf("%d%d%d%d%d", &n, &m, &l, &s, &E);
  for (int i = 0, x, y, z; i < m; i++) {
    scanf("%d%d%d", &x, &y, &z);
    add(x, y, z ? z : 1, z == 0);
  }
  SPFA();
  if (dis[E] > l) {
    printf("NO");
    return 0;
  }
  for (int k = 0; k < n; k++)
    for (int i = head[k]; ~i; i = e[i].next)
      if (i & 1)
        if (e[i].mk) {
          if (dis[E] == l) goto YJY;
          e[i ^ 1].v = e[i].v = l - dis[E] + 1;
          SPFA();
        }
  if (dis[E] != l) {
    printf("NO");
    return 0;
  }
YJY : {
  printf("YES\n");
  for (int k = 0; k < n; k++)
    for (int i = head[k]; ~i; i = e[i].next)
      if (i & 1) printf("%d %d %d\n", e[i ^ 1].to, e[i].to, e[i].v);
}
  return 0;
}
