#include <iostream>
#include <vector>
#include <queue>
using namespace std;

#define INF 100000000

struct edge {
	int to;
	int f;
	edge(int to_, int f_) {
		to = to_; f = f_;
	}
	edge(){}
};
struct status {
	int vertex;
	int cost;
	int c;
	status(int vertex_, int cost_, int c_) {
		vertex = vertex_; cost = cost_; c = c_;
	}
	status(){}
	bool operator<(const status & obj) const {
		if(this->c == obj.c)
			return this->c < obj.c;
		return this->cost > obj.cost;
	}
};

int main() {
	while(true) {
		int c, n, m, s, d;
		cin >> c >> n >> m >> s >> d;
		if(!(c || n || m || s || d))
			break;
		s--; d--;
		vector<vector<edge> > v(n);
		for(int i = 0; i < m; i++) {
			int a, b, f;
			cin >> a >> b >> f;
			a--; b--;
			v[a].push_back(edge(b,f));
			v[b].push_back(edge(a,f));
		}
		priority_queue<status> q;
		int cost[128][16];
		for(int i = 0; i < 128; i++)
			for(int j = 0; j < 16; j++)
				cost[i][j] = INF;
		q.push(status(s, 0, c));
		while(!q.empty()) {
			status cur;
			cur = q.top(); q.pop();

			if(cost[cur.vertex][cur.c] == INF) {
				cost[cur.vertex][cur.c] = cur.cost;
				for(int i = 0; i < v[cur.vertex].size(); i++) {
					if(cost[v[cur.vertex][i].to][cur.c] == INF) {
						q.push(status(v[cur.vertex][i].to, v[cur.vertex][i].f + cur.cost, cur.c));
					}
					if(cur.c > 0 && cost[v[cur.vertex][i].to][cur.c-1] == INF) {
						q.push(status(v[cur.vertex][i].to, v[cur.vertex][i].f / 2 + cur.cost, cur.c - 1));
					}
				}
			}
		}

		int ret = INF;
		for(int i = 0; i < m; i++) {
			ret = min(ret, cost[d][i]);
		}
		cout << ret << endl;
	}
}