#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define RFOR(i,a,b) for(int i=(b) - 1;i>=(a);i--)
#define REP(i,n) for(int i=0;i<(n);i++)
#define RREP(i,n) for(int i=n-1;i>=0;i--)

#define PB push_back
#define INF INT_MAX/3
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CLR(a) memset(a,0,sizeof(a))

typedef long long int ll;

using namespace std;

int c,n,m,s,d;
int rosen[101][101] = {-1};

int main(){
    while(true){
	scanf("%d%d%d%d%d",&c,&n,&m,&s,&d);
	if(c==0||n==0||m==0||s==0||d==0) break;
	memset(rosen,-1,sizeof(rosen));
	REP(i,m){
	    int a,b,f;
	    cin >> a >> b >> f;
	    rosen[a][b] = f;
	    rosen[b][a] = f;
	}
	int ans = 100000000;
	vector<bool>  used(n+1,false);
	vector<int> nanika;
	used[s] = true;
	queue<int> q;
        queue<string> st;
	vector<bool> u(n+1,false);
	u[s] = true;
	q.push(s);
	st.push(to_string(s));
	while(!q.empty()){
	    int p = q.front();
            string ss = st.front();
	    q.pop();
	    st.pop();
	    if(p == d){
		vector<int> v;
		int x = -1;
		int pre = s;
		REP(i,ss.size()){
		    if(ss[i]==' '){
			int var = stoi(ss.substr(x+1,i-1-x));
			v.PB(rosen[pre][var]);
			pre = var;
			x = i;
		    }
		}
		v.PB(rosen[pre][stoi(ss.substr(x+1,ss.size()-x-1))]);
		int sum = 0;
		int tc = min((int)(v.size()),c);
		sort(RALL(v));
		REP(i,tc){
		    v[i] /= 2;
		}
		REP(i,v.size()) sum += v[i];
		ans = min(ans,sum+1);
		continue;
	    }
	    FOR(i,1,n+1){
		if(rosen[p][i]>0 && !u[i]){
		    if(i!=d)
			u[i] = true;
		    q.push(i);
		    string temps = ss;
		    temps += " " + to_string(i);
		    st.push(temps);
		}
	    }
	}
	cout << ans << endl;
    }
    return 0;
}