#include <iostream>
#include <queue>
#include <algorithm>
#include <cstring>

#define MAX 1000000000
#define Debug(X) debug( __LINE__, X )
template<class T>
void debug( int line, T dbg ){
	std::cout << line << ": " << dbg << std::endl;
}

class State{
public:
	int p, s, c;
	State():p(0), s(0), c(0){}
	State(int P, int S, int C):p(P), s(S), c(C){}
	bool operator < (const State &s) const{
		return c > s.c;
	}
};

int c, n, m, s, d;
int route[101][101];
std::priority_queue<State> que;
bool used[101][11];


int main(){
	while( std::cin >> c >> n >> m >> s >> d, c * n * m * s * d ){
		for( int i = 0; i < 101 * 101; ++i )
			route[i / 101][i % 101] = MAX;
		
		memset( used, 0, sizeof( used ) );
		que = std::priority_queue<State>();

		int tmp[3];
		while( m-- ){
			int cnt = 3;
			while( cnt-- ) std::cin >> tmp[2 - cnt];

			route[tmp[0]][tmp[1]] = tmp[2];
			route[tmp[1]][tmp[0]] = tmp[2];
		}

		que.push(State( c, s, 0 ));

		while( true ){
			State data = que.top(); que.pop();

			if( used[data.s][data.p] )continue;
			used[data.s][data.p] = 1;

			if( data.s == d ){
				std::cout << data.c << std::endl;
				break;
			}

			for( int i = 1; i <= n; ++i ){
				if( i == data.s || route[data.s][i] == MAX )continue;

				if( data.p > 0 )
					que.push( State( data.p - 1, i, data.c + route[data.s][i] / 2 ) );

				que.push( State( data.p, i, data.c + route[data.s][i] ) );				
			}

		}

	}
}