#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));
  memset(last, -1, sizeof(last));
  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() {
  cout << "YES" << endl;
  for (int i = 0; i < p.size(); i++)
    cout << p[i].x << ' ' << g[p[i].x][int(p[i].y)].to << ' '
         << g[p[i].x][int(p[i].y)].cost << endl;
}
int main() {
  cin >> n >> m >> asked >> s >> t;
  int i, x, y;
  long long z;
  edge newedge;
  node newnode;
  for (i = 0; i < m; i++) {
    cin >> 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;
  int cnt;
  while (1) {
    dij(s, t);
    x = t;
    tmp = asked - d[t];
    cnt = 0;
    if (tmp == 0) {
      print();
      break;
    }
    if (tmp < 0) {
      cout << "NO\n";
      return 0;
    }
    while (x != s && tmp != 0) {
      if (last[x] == -1) break;
      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;
          cnt++;
          break;
        }
      x = last[x];
    }
    if (tmp > 0 || cnt == 0) {
      cout << "NO\n";
      return 0;
    }
  }
}
