#include <iostream>
#include <vector>

using namespace std;

#define INF 100000000

struct edge {
	int to, cost;
};

int main() {
	int c, n, m, s, d;
	while (cin >> c >> n >> m >> s >> d) {
		if (c == 0 && n == 0 && m == 0 && s == 0 && d == 0) {
			break;
		}
		vector<edge> ff[101];
		vector< vector<int> > ddd(n+1, vector<int>(n+1, INF));
		int a, b, f;
		for (int i = 0; i < m; i++) {
			cin >> a >> b >> f;
			edge e;
			e.to = b;
			e.cost = f;
			ff[a].push_back(e);
			e.to = a;
			ff[b].push_back(e);
			ddd[a][b] = ddd[b][a] = f;
		}
		for (int i = 1; i <= n; i++) {
			ddd[i][i] = 0;
		}
		for (int k = 1; k <= n; k++) {
			for (int i = 1; i <= n; i++) {
				for (int j = 1; j <= n; j++) {
					ddd[i][j] = min(ddd[i][j], ddd[i][k]+ddd[k][j]);
				}
			}
		}
		vector<int> isd[101];
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= n; j++) {
				if (ddd[i][j] != INF) {
					isd[i].push_back(j);
				}
			}
		}
		vector< vector< vector<int> > > dp(n+1, vector< vector<int> >(n+1, vector<int>(c+1, INF)));
		for (int i = 1; i <= n; i++) {
			dp[s][i][0] = ddd[s][i];
		}
		for (int k = 1; k <= c; k++) {
			for (int p = 0; p < isd[s].size(); p++) {
				int pp = isd[s][p];
				dp[s][pp][k] = dp[s][pp][k-1];
				for (int i = 0; i < isd[s].size(); i++) {
					int ii = isd[s][i];
					for (int j = 0; j < isd[ii].size(); j++) {
						int jj = isd[ii][j];
						for (int q = 0; q < ff[jj].size(); q++) {
							int qq = ff[jj][q].to;
							if (ddd[qq][pp] == INF) continue;
							if (dp[s][pp][k] > dp[s][ii][k-1]+ddd[ii][jj]+(ff[jj][q].cost/2)+ddd[qq][pp]) {
								dp[s][pp][k] = dp[s][ii][k-1]+ddd[ii][jj]+(ff[jj][q].cost/2)+ddd[qq][pp];
							}
						}
					}
				}
			}
		}
		cout << dp[s][d][c] << endl;
	}
	return 0;
}