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, asked, s, t;
struct edge {
  int cost, to, rev;
  bool mark;
};
vector<edge> g[1010];
struct node {
  int x;
  long long y;
};
vector<node> p;
bool operator>(node a, node b) { return a.y > b.y; };
priority_queue<node, vector<node>, greater<node> > q;
long long d[1010];
int last[1010];
void dij(int s, int t) {
  memset(d, -1, sizeof(d));
  node newnode, nownode;
  d[s] = 0;
  newnode.x = s;
  newnode.y = d[s];
  q.push(newnode);
  while (!q.empty()) {
    nownode = q.top();
    q.pop();
    if (nownode.y != d[nownode.x]) continue;
    for (int i = 0; i < g[nownode.x].size(); i++)
      if (nownode.y + g[nownode.x][i].cost < d[g[nownode.x][i].to] ||
          d[g[nownode.x][i].to] == -1) {
        d[g[nownode.x][i].to] = nownode.y + g[nownode.x][i].cost;
        last[g[nownode.x][i].to] = nownode.x;
        newnode.x = g[nownode.x][i].to;
        newnode.y = d[g[nownode.x][i].to];
        q.push(newnode);
      }
  }
}
void print() {
  printf("YES\n");
  for (int i = 0; i < p.size(); i++)
    printf("%d %d %I64d\n", p[i].x, g[p[i].x][int(p[i].y)].to,
           g[p[i].x][int(p[i].y)].cost);
}
int main() {
  scanf("%d %d %I64d %d %d\n", &n, &m, &asked, &s, &t);
  int i, x, y;
  long long z;
  edge newedge;
  node newnode;
  for (i = 0; i < m; i++) {
    scanf("%d %d %I64d\n", &x, &y, &z);
    if (z != 0) {
      newedge.cost = z;
      newedge.mark = 0;
    } else {
      newedge.cost = 1;
      newedge.mark = 1;
    }
    newedge.to = y;
    g[x].push_back(newedge);
    g[x][g[x].size() - 1].rev = g[y].size();
    newedge.to = x;
    g[y].push_back(newedge);
    g[y][g[y].size() - 1].rev = g[x].size() - 1;
    newnode.x = x;
    newnode.y = g[x].size() - 1;
    p.push_back(newnode);
  }
  long long tmp;
  while (1) {
    dij(s, t);
    x = t;
    tmp = asked - d[t];
    if (tmp == 0) {
      print();
      break;
    }
    if (tmp < 0) {
      printf("NO\n");
      return 0;
    }
    while (x != s && tmp != 0) {
      for (i = 0; i < g[x].size(); i++)
        if (g[x][i].to == last[x]) {
          if (!g[x][i].mark) break;
          g[x][i].cost += tmp;
          tmp = 0;
          if (g[x][i].cost > 1000000000) {
            tmp = g[x][i].cost - 1000000000;
            g[x][i].cost = 1000000000;
          }
          g[g[x][i].to][g[x][i].rev].cost = g[x][i].cost;
          break;
        }
      x = last[x];
    }
    if (tmp > 0) {
      printf("NO\n");
      return 0;
    }
  }
}
