#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iterator>
#include <bitset>
//#include <utility>
//#include <memory>
//#include <functional>
//#include <deque>
//#include <cctype>
//#include <ctime>
//#include <numeric>
//#include <list>
//#include <iomanip>

//#if __cplusplus >= 201103L
//#include <array>
//#include <tuple>
//#include <initializer_list>
//#include <unordered_set>
//#include <unordered_map>
//#include <forward_list>
//
//#define cauto const auto&
//#else

//#endif

using namespace std;


namespace{
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<long long> vll, vLL;
typedef vector<vector<long long> > vvll, vvLL;

#define VV(T) vector<vector< T > >

template <class T>
void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()){
    v.assign(a, vector<T>(b, t));
}

template <class F, class T>
void convert(const F &f, T &t){
    stringstream ss;
    ss << f;
    ss >> t;
}


#define reep(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) reep((i),0,(n))
#define ALL(v) (v).begin(),(v).end()
#define PB push_back
#define F first
#define S second
#define mkp make_pair
#define RALL(v) (v).rbegin(),(v).rend()


#define MOD 1000000007LL
#define EPS 1e-8
static const int INF=1<<24;

void mainmain(){
	int c,n,m,d,s;
	while(cin>>c>>n>>m>>s>>d,c||n||m||s||d){
		vvint dp;
		initvv(dp,n,c+1,-1);
		VV(pii) vv(n);
		rep(i,m){
			int a,b,f;
			cin>>a>>b>>f;
			vv[a-1].PB(mkp(b-1,f));
			vv[b-1].PB(mkp(a-1,f));
		}
		priority_queue<pair<int,pii>> pq;
		pq.push(mkp(0,pii(s-1,c)));
		while(!pq.empty()){
			pair<int,pii> top=pq.top();
			pq.pop();
			if(dp[top.S.F][top.S.S]!=-1){
				continue;
			}	
			dp[top.S.F][top.S.S]=-top.F;
			rep(i,vv[top.S.F].size()){
				if(dp[vv[top.S.F][i].F][top.S.S]==-1){
					pq.push(mkp(top.F-vv[top.S.F][i].S,pii(vv[top.S.F][i].F,top.S.S)));
				}
				if(top.S.S>=1&&dp[vv[top.S.F][i].F][top.S.S-1]==-1){
					pq.push(mkp(top.F-vv[top.S.F][i].S/2,pii(vv[top.S.F][i].F,top.S.S-1)));
				}
			}
		}
		int ans=INF;
		rep(i,dp[d-1].size()){
			ans=min(ans,dp[d-1][i]);
		}
		cout<<ans<<endl;
	}
}



}
main() try{
    mainmain();
}
catch(...){
}