//Solution for aoj:0212 Highway Express Bus
#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<functional>
using namespace std;
typedef pair<int, int>P;
typedef pair < P, int > PP;
#define f first
#define s second

//struct S {
//	int cost, to, num;
//	S(int c, int t, int n) : cost(c), to(t), num(n){}
//	bool operator>(const S &s) const {
//		return cost > s.cost;
//	}
//};

const int INF = 1 << 29;
int c, n, m, s, d, ans;
int tocost[1000][100];
vector<P> town[1000];


void dijkstra(){
	priority_queue<PP, vector<PP>, greater<PP> > pq;
	pq.push({ { 0, s }, c });
	while (!pq.empty()){
		PP a = pq.top();
		pq.pop();
		for (int i = 0; i < town[a.f.s].size(); i++){
			int tt = town[a.f.s][i].f, cc = town[a.f.s][i].s;
			if (tocost[tt][a.s] > cc + a.f.f){
				tocost[tt][a.s] = cc + a.f.f;
				pq.push({ { cc + a.f.f, tt }, a.s });
			}
			if (a.s&&tocost[tt][a.s-1] > cc/2 + a.f.f){
				tocost[tt][a.s-1] = cc/2 + a.f.f;
				pq.push({ { cc / 2 + a.f.f, tt }, a.s - 1 });
			}
		}
	}
}
	int main(){
		while (cin >> c >> n >> m >> s >> d&&c&&n&&m&&s){
			for (int i = 0; i < 1000; i++)
				fill(tocost[i], tocost[i] + 100, INF);
			tocost[s][c] = 0;
			ans = INF;
			for (int i = 0; i < 1000; i++)
				town[i].clear();
			for (int i = 0; i < m; i++){
				int a, b, c;
				cin >> a >> b >> c;
				town[a].push_back({ b, c });
				town[b].push_back({ a, c });
			}
			dijkstra();
			for (int i = 0; i <= c; i++)
				ans = min(ans, tocost[d][i]);
			cout << ans << endl;
		}
		return 0;
	}