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;
int n, m, s, t;
long long val[20010], dis[2000], l;
int sum = 0, des[20010], nxt[20010], e[20010], fst[2000];
int pre[2000], pree[2000];
bool b[20010], f[20010];
void add(int x, int y, long long z) {
  des[++sum] = y, val[sum] = z, nxt[sum] = fst[x], fst[x] = sum,
  e[sum] = sum + 1;
  if (z == 0) val[sum] = 233333333333, b[sum] = 1;
  des[++sum] = x, val[sum] = z, nxt[sum] = fst[y], fst[y] = sum,
  e[sum] = sum - 1;
  if (z == 0) val[sum] = 233333333333, b[sum] = 1;
}
void pr() {
  memset(f, 0, sizeof f);
  for (int i = 1; i <= sum; ++i)
    if (!f[i]) {
      printf("%d %d %I64d\n", des[e[i]], des[i], val[i]);
      f[i] = f[e[i]] = 1;
    }
}
int main() {
  scanf("%d%d%I64d%d%d", &n, &m, &l, &s, &t);
  memset(b, 0, sizeof b);
  for (int i = 1; i <= m; ++i) {
    int x, y;
    long long z;
    scanf("%d%d%I64d", &x, &y, &z);
    add(x, y, z);
  }
  for (int i = 0; i < n; ++i) dis[i] = 233333333333;
  queue<int> q;
  q.push(s);
  dis[s] = 0;
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (int i = fst[x]; i; i = nxt[i]) {
      int y = des[i];
      if (dis[x] + val[i] < dis[y]) dis[y] = dis[x] + val[i], q.push(y);
    }
  }
  if (dis[t] < l) {
    printf("NO");
    return 0;
  }
  if (dis[t] == l) {
    printf("YES\n");
    pr();
    return 0;
  }
  for (int i = 1; i <= sum; ++i)
    if (b[i]) val[i] = 1;
  for (int i = 0; i < n; ++i) dis[i] = 233333333333;
  q.push(s);
  dis[s] = 0;
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    for (int i = fst[x]; i; i = nxt[i]) {
      int y = des[i];
      if (dis[x] + val[i] < dis[y]) {
        dis[y] = dis[x] + val[i], pre[y] = x, pree[y] = i;
        q.push(y);
      }
    }
  }
  if (dis[t] > l) {
    printf("NO");
    return 0;
  }
  while (dis[t] < l) {
    for (int i = t; i != s; i = pre[i]) {
      if (b[pree[i]]) {
        val[pree[i]] += l - dis[t], val[e[pree[i]]] += l - dis[t];
        break;
      }
    }
    for (int i = 0; i < n; ++i) dis[i] = 233333333333;
    q.push(s);
    dis[s] = 0;
    while (!q.empty()) {
      int x = q.front();
      q.pop();
      for (int i = fst[x]; i; i = nxt[i]) {
        int y = des[i];
        if (dis[x] + val[i] < dis[y]) {
          dis[y] = dis[x] + val[i], pre[y] = x, pree[y] = i;
          q.push(y);
        }
      }
    }
  }
  printf("YES\n");
  pr();
  return 0;
}
