#include<bits/stdc++.h>
typedef long long ll;
typedef long double ld;
using namespace std;

int n,m,l,s,t;
const int MX=1e3+4;
vector<int> adj[MX];
ll weigh[1005][1005];
vector<pair<int,int> > un;
priority_queue<pair<ll, int> > pq;
bool vis[1002];
ll dijktra()
{
    memset(vis,0,sizeof vis);
    pq.push({0,s});
    while(!pq.empty())
    {
    int nx=pq.top().second;
    if(vis[nx])
    {
        pq.pop();
        continue;
    }
    vis[nx]=1;
    if(nx==t)
    {
        return -1*pq.top().first;
    }
    for(int i=0;i<adj[nx].size();i++)
    {
        int y=adj[nx][i];
        pq.push({pq.top().first+ (-1*weigh[y][nx]),y});
    }
    pq.pop();
    }
}
int main()
{
  cin>>n>>m>>l>>s>>t;
  for(int i=0;i<m;i++)
  {
      int x,y,z;
      scanf("%d%d%d",&x,&y,&z);
      adj[x].push_back(y);
      adj[y].push_back(x);
      if(z==0){
            un.push_back({x,y});
            if(weigh[x][y]!=0)continue;
            weigh[x][y]=1e9+3;
      weigh[y][x]=1e9+3;
      continue;
      }
      if(weigh[x][y]<z&&weigh[x][y]!=0)continue;
      weigh[x][y]=z;
      weigh[y][x]=z;

  }
  if(dijktra()==l)
  {
      cout<<"YES"<<endl;
               for(int c=0;c<1001;c++)
                    for(int w=c+1;w<1001;w++)
                    if(weigh[c][w])
                    cout<<c<<' '<<w<<' '<<weigh[c][w]<<endl;;
               return 0;
  }
  for(int i=0;i<un.size();i++)
  {
      int a=un[i].first;
      int b=un[i].second;
      ll en,st,mid;
      en=weigh[a][b];
       st=1;
      while(st<=en)
      {
          mid=(st+en)/2;
           while(!pq.empty())pq.pop();
          weigh[a][b]=mid;
          weigh[b][a]=mid;

          ll re =dijktra();
           if(re<l)
          {
              st=mid+1;
          }
          else if (re>l)
          {
              en=mid-1;
          }
          else{
                cout<<"YES"<<endl;
               for(int c=0;c<1001;c++)
                    for(int w=c+1;w<1001;w++)
                    if(weigh[c][w])
                    cout<<c<<' '<<w<<' '<<weigh[c][w]<<endl;;
               return 0;
          }
      }

  }
cout<<"NO";
               return 0;
}