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 N = int(1e3) + 10;
int n, m, s, t;
long long int L;
vector<int> v[N];
vector<pair<int, pair<int, long long int> > > edge;
vector<long long int> w[N];
long long int dist[N];
int p[N];
long long int mw[N][N];
map<pair<int, int>, long long int> cnt;
bool ok = false;
long long int INF = 1e18;
void solve(long long int k) {
  for (int i = 0; i < n; i++) dist[i] = INF;
  memset(p, -1, sizeof p);
  priority_queue<pair<long long int, int> > pq;
  pq.push({0LL, s});
  dist[s] = 0LL;
  p[s] = s;
  while (!pq.empty()) {
    int u = pq.top().second;
    pq.pop();
    if (u == t) break;
    for (int i = 0; i < v[u].size(); i++) {
      int adj = v[u][i];
      long long int peso = mw[u][adj];
      if (peso == 0LL) peso = k;
      if (dist[adj] > dist[u] + peso) {
        dist[adj] = dist[u] + peso;
        pq.push({-dist[adj], adj});
        p[adj] = u;
      }
    }
  }
}
int main() {
  scanf("%d %d %lld %d %d", &n, &m, &L, &s, &t);
  for (int i = 0; i < m; i++) {
    int x, y;
    long long int z;
    scanf("%d %d %lld", &x, &y, &z);
    v[x].push_back(y);
    w[x].push_back(z);
    v[y].push_back(x);
    w[y].push_back(z);
    edge.push_back({x, {y, z}});
    mw[x][y] = mw[y][x] = z;
  }
  solve(0);
  if (dist[t] > L) {
    printf("NO\n");
    return 0;
  }
  solve(1);
  long long int ans = dist[t];
  if (dist[t] > L) {
    printf("NO\n");
    return 0;
  }
  for (int i = t; i != s; i = p[i]) {
    int x = i;
    int y = p[i];
    long long int peso = mw[x][y];
    if (!peso && !ok) {
      if (L - ans + 1 > 0) {
        ok = true;
        cnt[{x, y}] = cnt[{y, x}] = L - ans + 1;
        mw[x][y] = mw[y][x] = L - ans + 1;
      } else {
        cnt[{x, y}] = cnt[{y, x}] = 1;
        mw[x][y] = mw[y][x] = 1;
      }
    } else if (!peso && ok) {
      cnt[{x, y}] = cnt[{y, x}] = 1;
      mw[x][y] = mw[y][x] = 1;
    } else {
      cnt[{x, y}] = cnt[{y, x}] = peso;
    }
  }
  solve(L + 1);
  if (dist[t] != L) {
    printf("NO\n");
    return 0;
  }
  printf("YES\n");
  for (int i = 0; i < m; i++) {
    int x = edge[i].first;
    int y = edge[i].second.first;
    long long int z = mw[x][y];
    if (cnt.find({x, y}) == cnt.end()) {
      if (z == 0) {
        printf("%d %d %lld", x, y, L + 1);
      } else {
        printf("%d %d %lld", x, y, z);
      }
    } else if (cnt.find({x, y}) != cnt.end()) {
      printf("%d %d %lld", x, y, cnt[{x, y}]);
    }
    printf("\n");
  }
  return 0;
}
