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_int = 0x3f3f3f3f;
const long long INF_LL = 0x7fffffffffffffff;
const double oo = 10e9;
const double eps = 10e-7;
const double PI = acos(-1.0);
const long long MAXN = 1100;
struct node {
  long long to;
  long long w;
};
vector<node> v[MAXN];
long long n, m, L, s, t;
map<pair<long long, long long>, long long> mp;
long long d[MAXN];
long long vis[MAXN];
long long path[MAXN];
void spfa() {
  queue<long long> q;
  memset(vis, (0), sizeof(vis));
  memset(path, (-1), sizeof(path));
  for (long long i = 0; i < n; i++) d[i] = INF_LL;
  d[s] = 0;
  q.push(s);
  while (!q.empty()) {
    long long vv = q.front();
    q.pop();
    vis[vv] = 0;
    for (long long i = 0; i < v[vv].size(); i++) {
      long long u = v[vv][i].to, w = v[vv][i].w;
      if (d[u] > d[vv] + w) {
        d[u] = d[vv] + w;
        path[u] = vv;
        if (!vis[u]) {
          q.push(u);
          vis[u] = 1;
        }
      }
    }
  }
}
struct aans {
  long long u;
  long long v;
  long long w;
} ans[10010];
int main() {
  scanf("%I64d%I64d%I64d%I64d %I64d ", &n, &m, &L, &s, &t);
  long long f, tt, w;
  for (long long i = 0; i < m; i++) {
    scanf("%I64d %I64d %I64d ", &f, &tt, &w);
    v[f].push_back(node{tt, w});
    v[tt].push_back(node{f, w});
    if (w == 0) {
      mp[make_pair(f, tt)] = 1;
      mp[make_pair(tt, f)] = 1;
    }
    ans[i].u = f;
    ans[i].v = tt;
    ans[i].w = w;
  }
  spfa();
  if (d[t] > L) {
    printf("NO\n");
    return 0;
  }
  long long q = t;
  long long cnt = 0;
  while (path[q] != -1) {
    if (mp[make_pair(q, path[q])] == 1) cnt++;
    q = path[q];
  }
  long long c = L - d[t] - cnt;
  if (c < 0 || (c > 0 && cnt == 0)) {
    printf("NO\n");
    return 0;
  }
  printf("YES\n");
  q = t;
  while (path[q] != -1 && cnt) {
    if (mp[make_pair(q, path[q])] == 1) {
      mp[make_pair(t, path[t])] += c;
      mp[make_pair(path[t], t)] += c;
      break;
    }
    q = path[q];
  }
  for (long long i = 0; i < m; i++) {
    if (ans[i].w != 0)
      printf("%I64d  %I64d  %I64d \n", ans[i].u, ans[i].v, ans[i].w);
    else
      printf("%I64d  %I64d  %I64d \n", ans[i].u, ans[i].v,
             mp[make_pair(ans[i].u, ans[i].v)]);
  }
  return 0;
}
