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 toit, next, cap, from;
} road[100010];
int q[300010], n, m, l, s, t, cnt = 1, dis1[100010], dis2[100010];
int listt[100010], vis[10010], in[100010];
inline void add(int u, int v, int w) {
  road[++cnt].toit = v;
  road[cnt].next = listt[u];
  listt[u] = cnt;
  road[cnt].cap = w;
  road[cnt].from = u;
}
inline void spfa(int s) {
  dis1[s] = 0;
  int head = 0, tail = 1;
  q[tail] = s;
  in[s] = 1;
  while (head < tail) {
    int u = q[++head];
    for (int w = listt[u]; w; w = road[w].next) {
      int v = road[w].toit;
      if (dis1[v] <= dis1[u] + road[w].cap) continue;
      dis1[v] = dis1[u] + road[w].cap;
      if (in[v]) continue;
      in[v] = 1;
      q[++tail] = v;
    }
    in[u] = 0;
  }
}
inline void SPFA(int s) {
  dis2[s] = 0;
  int head = 0, tail = 1;
  q[tail] = s;
  in[s] = 1;
  while (head < tail) {
    int u = q[++head];
    for (int w = listt[u]; w; w = road[w].next) {
      int v = road[w].toit;
      if (vis[w])
        road[w xor 1].cap = road[w].cap =
            max(road[w].cap, l - dis1[v] - dis2[u]);
      if (dis2[v] <= dis2[u] + road[w].cap) continue;
      dis2[v] = dis2[u] + road[w].cap;
      if (in[v] == 1) continue;
      in[v] = 1;
      q[++tail] = v;
    }
    in[u] = 0;
  }
}
int main() {
  memset(dis1, 127 / 3, sizeof(dis1));
  memset(dis2, 127 / 3, sizeof(dis2));
  memset(vis, 0, sizeof(vis));
  scanf("%d%d%d%d%d", &n, &m, &l, &s, &t);
  int a, b, c;
  for (int i = 1; i <= m; i++) {
    scanf("%d%d%d", &a, &b, &c);
    if (c == 0) vis[cnt + 1] = 1, vis[cnt + 2] = 1, c = 1;
    add(a, b, c);
    add(b, a, c);
  }
  memset(in, 0, sizeof(in));
  spfa(t);
  memset(in, 0, sizeof(in));
  SPFA(s);
  if (dis2[t] != l) {
    printf("NO");
    return 0;
  }
  printf("YES\n");
  for (int i = 2; i <= m * 2; i++)
    if (i % 2 == 0)
      printf("%d %d %d\n", road[i].from, road[i].toit, road[i].cap);
  return 0;
}
