#include <iostream>
#include <queue>

#define INF 1e9

using namespace std;

struct Edge {
	int to, cost;
};
struct Node {
	int now, rest, cost;
};
bool operator <(const Node& n1, const Node& n2) {
	return n1.cost < n2.cost;
}
bool operator >(const Node& n1, const Node& n2) {
	return n1.cost > n2.cost;
}

int main() {
	int c, n, l, s, d;
	while ( cin >> c >> n >> l >> s >> d, c || n || l || s || d ) {
		--s, --d;

		vector<Edge> m[100];
		for (int i = 0; i < l; ++i) {
			int a, b, f; cin >> a >> b >> f; --a, --b;
			m[a].push_back( (Edge){ b, f } );
			m[b].push_back( (Edge){ a, f } );
		}

		int ans[100][11]; fill(&ans[0][0], &ans[0][0]+100*11, INF);
		priority_queue<Node, vector<Node>, greater<Node> > Q; Q.push( (Node){s, c, 0} );
		while ( !Q.empty() ) {
			Node node = Q.top(); Q.pop();
			if (node.cost >= ans[node.now][node.rest]) continue;
			ans[node.now][node.rest] = node.cost;

			for (int i = 0; i < m[node.now].size(); ++i) {
				Edge& e = m[node.now][i];
				if (node.cost+e.cost < ans[e.to][node.rest]) {
					Q.push( (Node){ e.to, node.rest, node.cost+e.cost } );
				}

				if (node.rest > 0) {
					if (node.cost+e.cost/2 < ans[e.to][node.rest-1]) {
						Q.push( (Node){ e.to, node.rest-1, node.cost+e.cost/2 } );
					}
				}
			}
		}
		int a = INF;
		for (int i = 0; i <= c; ++i) a = min(a, ans[d][i]);
		cout << a << endl;
	}
}