1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstdlib>
 4 #include <cmath>
 5 #include <algorithm>
 6 #include <cstring>
 7 #include <stack>
 8 #include <cctype>
 9 #include <queue>
10 #include <string>
11 #include <vector>
12 #include <set>
13 #include <map>
14 #include <climits>
15 #define lson rt<<1,l,mid
16 #define rson rt<<1|1,mid+1,r
17 #define fi first
18 #define se second
19 #define ping(x,y) ((x-y)*(x-y))
20 #define mst(x,y) memset(x,y,sizeof(x))
21 #define mcp(x,y) memcpy(x,y,sizeof(y))
22 using namespace std;
23 #define gamma 0.5772156649015328606065120
24 #define mod 1000000007
25 #define inf 0x3f3f3f3f
26 #define N 1005050
27 #define maxn 20005
28 typedef pair<int,int> PII;
29 typedef long long LL;
30
31 int n,m,k,x,y,v;
32 int S,T,L;
33 int head[N],hcnt;
34 struct Node{
35     int to,nxt,v;
36 }node[maxn];
37 int d[N],vis[N],s[maxn];
38 vector<int>eg;  ///存重构边
39 queue<int>q;
40 int spfa(){
41     for(int i=0;i<n;++i) d[i]=(int)1e9+1; d[S]=0;
42     mst(vis,0); q.push(S);
43     while(!q.empty()){
44         int x=q.front();q.pop(); vis[x]=0;
45         for(int i=head[x];~i;i=node[i].nxt){
46             int e=node[i].to;
47             if(d[e]>d[x]+node[i].v){
48                 d[e]=d[x]+node[i].v;
49                 if(!vis[e]){vis[e]=1;q.push(e);}
50             }
51         }
52     }
53     return d[T];
54 }
55 int check(LL sum){  ///判断是否合法
56     for(int u:eg){
57         node[u].v=node[u|1].v=1+min(sum,1000000000ll);
58                     ///给每个重构边分配权值
59         sum-=node[u].v-1;
60     }
61     return spfa();
62 }
63 inline void add(int x,int y,int v){
64     node[hcnt].to=y;node[hcnt].nxt=head[x];node[hcnt].v=v;head[x]=hcnt++;
65 }
66 int main(){
67     int i,j,group;
68     mst(head,-1);
69     scanf("%d%d%d%d%d",&n,&m,&L,&S,&T);
70     for(i=1;i<=m;++i){
71         scanf("%d%d%d",&x,&y,&v);
72         if(!v)eg.push_back(hcnt);
73         s[hcnt]=x;
74         add(x,y,v);
75         add(y,x,v);
76     }
77     LL l=0,r=eg.size()*LL(1e9);
78     if(check(0)>L||check(r)<L)return 0*printf("NO\n");
79     LL ans;
80     while(l<=r){
81         LL mid=l+r>>1,temp=check(mid);
82         if(temp>L)ans=mid,r=mid-1;
83         else if(temp<L)l=mid+1;
84         else break;
85     }
86     printf("YES\n");
87     for(i=0;i<m*2;i+=2)printf("%d %d %d\n",s[i],node[i].to,node[i].v);
88     return 0;
89 }