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

// God & me
// Don't forget me ...
#include <bits/stdc++.h>
#define pb push_back
#define X first
#define Y second
#define int long long
using namespace std;
template <class T, class L> bool smax(T &x, L y){  return x < y ? ( x = y, 1) : 0;  }
template <class T, class L> bool smin(T &x, L y){  return y < x ? ( x = y, 1) : 0;  }
typedef pair <int, int> pii;
typedef long long ll;

const int maxn = 1e4 + 17;
int n, m, l, s, t, par[maxn], d[maxn], edin[maxn];
vector<pii> g[maxn];
map<pii, int> mp;
pair<pii, int> e[maxn];
priority_queue<pii, vector<pii>, greater<pii> > pq;
bool mark[maxn], bad[maxn];
void dij(){
    memset(d, 127, sizeof d), memset(par, -1, sizeof par), memset(mark, 0, sizeof mark);
    d[s] = 0;
    pq.push({0, s});
    while(pq.size()){
	int v = pq.top().Y, dis = pq.top().X;  pq.pop();
	if(mark[v])  continue;
	mark[v] = 1;
	for(auto &e : g[v])
	    if(smin(d[e.X], dis + e.Y))
		par[e.X] = v, pq.push({d[e.X], e.X});
    }
}
main(){
    ios::sync_with_stdio(0), cin.tie(0);
    cin >> n >> m >> l >> s >> t;
    for(int v, u, w, i = 0; i < m; i++){
	cin >> v >> u >> w;
	if(w == 0)  w = 1, bad[i] = 1;
	g[v].pb({u, w}), g[u].pb({v, w});
	mp[minmax(v, u)] = i;
	e[i] = {{v, u}, w};
    }
    dij();
    if(par[t] == -1)  return cout << "NO\n", 0;
    int best = 0;
    for(int v = t; v != s; v = par[v])
	best += e[ mp[minmax(v, par[v])] ].Y;
    if(best > l)  return cout << "NO\n", 0;
    for(int i = 0; i < m; i++)
	if(bad[i])  e[i].Y = 1e14;
    for(int v = t, done = 1; v != s; v = par[v])
    	if(bad[ mp[minmax(v, par[v])] ])
	    e[ mp[ minmax(v, par[v]) ] ].Y = 1 + done * (l - best), done = 0;
    for(int i = 0; i < n; i++)  g[i].clear();
    for(int v, u, w, i = 0; i < m; i++){
	v = e[i].X.X, u = e[i].X.Y, w = e[i].Y;
	g[v].pb({u, w}), g[u].pb({v, w});
    }
    dij();
    if(d[t] != l)  return cout << "NO\n", 0;
    cout << "YES\n";
    for(int i = 0; i < m; i++)
	cout << e[i].X.X << ' ' << e[i].X.Y << ' ' << e[i].Y << '\n';
    return 0;
}
