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;
const int INF = 1e9 + 1;
const int mxn = 10010;
int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
struct edge {
  int v, nxt, w;
} e[mxn << 1];
int hd[mxn], mct = 1;
void add_edge(int u, int v, int w) {
  e[++mct].v = v;
  e[mct].nxt = hd[u];
  e[mct].w = w;
  hd[u] = mct;
  return;
}
long long dis[mxn], dis2[mxn];
bool inq[mxn];
void SPFA(int S) {
  memset(dis, 0x3f, sizeof dis);
  queue<int> q;
  q.push(S);
  dis[S] = 0;
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    inq[u] = 0;
    for (int i = hd[u]; i; i = e[i].nxt) {
      int v = e[i].v;
      if (dis[v] > dis[u] + e[i].w) {
        dis[v] = dis[u] + e[i].w;
        if (!inq[v]) {
          inq[v] = 1;
          q.push(v);
        }
      }
    }
  }
  return;
}
struct EG {
  int x, y, w;
  bool use;
} ve[mxn];
int id[mxn], cnt = 0;
int n, m, S, T, L;
int main() {
  int i, j;
  n = read();
  m = read();
  L = read();
  S = read() + 1;
  T = read() + 1;
  int u, v, w;
  for (i = 1; i <= m; i++) {
    u = read() + 1;
    v = read() + 1;
    w = read();
    ve[i] = (EG){u, v, w, 0};
    add_edge(u, v, w);
    add_edge(v, u, w);
    if (!w) {
      ve[i].use = 1;
      id[i] = mct - 1;
    }
  }
  for (i = 1; i <= m; i++)
    if (id[i]) e[id[i]].w = e[id[i] ^ 1].w = 1, ve[i].w = 1;
  SPFA(S);
  if (dis[T] > L) {
    printf("NO\n");
    return 0;
  }
  for (i = 1; i <= m; i++)
    if (id[i]) e[id[i]].w = e[id[i] ^ 1].w = INF, ve[i].w = INF;
  SPFA(S);
  if (dis[T] < L) {
    printf("NO\n");
    return 0;
  }
  printf("YES\n");
  if (dis[T] > L) {
    for (i = 1; i <= m; i++) {
      if (id[i]) {
        ve[i].w = e[id[i]].w = e[id[i] ^ 1].w = 1;
        SPFA(S);
        if (dis[T] <= L) {
          ve[i].w = e[id[i]].w = e[id[i] ^ 1].w = 1 + L - dis[T];
          break;
        }
      }
    }
  }
  for (i = 1; i <= m; i++)
    printf("%d %d %d\n", ve[i].x - 1, ve[i].y - 1, ve[i].w);
  return 0;
}
