Go: package main

import (
	"container/heap"
	"fmt"
)

type Node struct {
	NowPosition          int
	DiscountTicketTCount int
	Amount               int
}

type PriorityQueueNode []*Node

func (pq PriorityQueueNode) Len() int {
	return len(pq)
}

func (pq PriorityQueueNode) Less(i, j int) bool {
	return pq[i].Amount < pq[j].Amount
}

func (pq PriorityQueueNode) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
}

func (pq *PriorityQueueNode) Push(node interface{}) {
	*pq = append(*pq, node.(*Node))
}

func (pq *PriorityQueueNode) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	*pq = old[0 : n-1]
	return item
}

type Point struct {
	NextPoint int
	Fee       int
}

type Memo struct {
	NowPoint             int
	DiscountTicketTCount int
}

func main() {
	var c, n, m, s, d int
	var a, b, f int

	for {
		fmt.Scan(&c, &n, &m, &s, &d)
		if c == 0 && n == 0 && m == 0 && s == 0 && d == 0 {
			break
		}
		s--
		d--
		pointMap := make([][]Point, n)
		for i := 0; i < n; i++ {
			pointMap[i] = make([]Point, 0, n)
		}
		for i := 0; i < m; i++ {
			fmt.Scan(&a, &b, &f)
			a--
			b--
			pointMap[a] = append(pointMap[a], Point{NextPoint: b, Fee: f})
			pointMap[b] = append(pointMap[b], Point{NextPoint: a, Fee: f})
		}
		pq := make(PriorityQueueNode, 0, m)
		start := Node{NowPosition: s, DiscountTicketTCount: c, Amount: 0}
		heap.Push(&pq, &start)
		memo := make(map[Memo]int)
		for len(pq) != 0 {
			now := heap.Pop(&pq).(*Node)
			if now.NowPosition == d {
				fmt.Println(now.Amount)
				break
			}
			memo[Memo{NowPoint: now.NowPosition, DiscountTicketTCount: now.DiscountTicketTCount}] = now.Amount
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
					memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
						memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
						heap.Push(&pq, next)
					}
				}
			}
		}
		//runtime.GC()
	}
}

C++: //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;


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 << 30;
int c, n, m, s, d, ans;
int tocost[101][11];
vector<P> town[501];
priority_queue<S, vector<S>, greater<S> > pq;


void dijkstra(){
	while (!pq.empty()){
		S a = pq.top();
		pq.pop();
		for (int i = 0; i < town[a.to].size(); i++){
			int tt = town[a.to][i].first, cc = town[a.to][i].second;
			if (tocost[tt][a.num] > cc + a.cost){
				tocost[tt][a.num] = cc + a.cost;
				pq.push(S( cc + a.cost, tt, a.num ));
			}
			if (a.num>0&&tocost[tt][a.num-1] > cc/2 + a.cost){
				tocost[tt][a.num-1] = cc/2 + a.cost;
				pq.push(S( cc/2 + a.cost, tt, a.num-1 ));
			}
		}
	}
}
	int main(){
		while (cin >> c >> n >> m >> s >> d&&c&&n&&m&&s){
			for (int i = 0; i < 101; i++)
				fill(tocost[i], tocost[i] + 11, INF);
			tocost[s][c] = 0;
			ans = INF;
			while (pq.size())
				pq.pop();
			for (int i = 0; i < n; i++)
				town[i].clear();
			for (int i = 0; i < m; i++){
				int a, b, c;
				cin >> a >> b >> c;
				town[a].push_back(P( b, c ));
				town[b].push_back(P( a, c ));
			}
			pq.push(S( 0, s, c ));
			dijkstra();
			for (int i = 0; i <= c; i++)
				ans = min(ans, tocost[d][i]);
			cout << ans << endl;
		}
		return 0;
	}

C++: // AOJ 0212
#include<cstdio>
#include<algorithm>
#include<functional>
#include<vector>
#include<queue>
#define rep(i,a) for( int i = 0; i != (a); ++i )

typedef std::pair<int, int> P;
typedef std::pair<P, int> PP;

const int INF = 1 << 30;

int c, n, m, s, d;	
std::vector<P> G[100];
int dist[100][11];

int dijkstra( int s )
{
	std::fill( (int*)dist, (int*)dist+100, INF );
	dist[s][0] = 0;
	std::priority_queue<PP, std::vector<PP>, std::greater<PP> > pque;
	pque.push( PP( P( s, 0 ), 0 ) );
	while( !pque.empty() )
	{
		PP p = pque.top(); pque.pop();
		int v = p.first.first, cost = p.first.second, tic = p.second;

		if( dist[v][tic] < cost )
			continue;

		rep( i, G[v].size() )
		{
			P &e = G[v][i];

			if( tic < c && dist[e.first][tic+1] > dist[v][tic]+e.second/2 )
			{
				dist[e.first][tic+1] = dist[v][tic]+e.second/2;
				pque.push( PP( P( e.first, dist[e.first][tic+1] ), tic+1 ) );
			}

			if( dist[e.first][tic] > dist[v][tic]+e.second )
			{
				dist[e.first][tic] = dist[v][tic]+e.second;
				pque.push( PP( P( e.first, dist[e.first][tic] ), tic ) );
			}
		}
	}

	return *std::min_element( dist[d], dist[d]+11 );
}

int main()
{
	while( scanf( "%d%d%d%d%d", &c, &n, &m, &s, &d ), c|n|m|s|d )
	{
		--s; --d;
		rep( i, 100 )
			G[i].clear();

		rep( i, m )
		{
			int a, b, f;
			scanf( "%d%d%d", &a, &b, &f );
			--a; --b;
			G[a].push_back( P( b, f ) );
			G[b].push_back( P( a, f ) );
		}

		printf( "%d\n", dijkstra( s ) );
	}

	return 0;
}

C++: #include <bits/stdc++.h>
#define INF (1<<29)
#define all(c) (c).begin(),(c).end()
#define pb(c) push_back(c)
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
typedef pair<int, P> PP;

int dis[111][111];
int c, n, m, s, d;
int next[111][111];

void dfs(int cur, int sum, int cost){
  if(next[cur][sum] < cost) return;
  next[cur][sum] = cost;
  for(int i = 0; i < n; i++){
    if(dis[cur][i] == (1<<29)) continue;
    if(sum > 0) dfs(i, sum-1, cost+(dis[cur][i]/2));
    dfs(i, sum, cost+dis[cur][i]);
  }
}

int main(){
  ios::sync_with_stdio(false);

  while(cin >> c >> n >> m >> s >> d && (c||n||m||s||d)){

    for(int i = 0; i < 111; i++){
      for(int j = 0; j < 111; j++){
        dis[i][j] = next[i][j] = (1<<29);
      }
    }

    for(int i = 0; i < m; i++){
      int a, b, f;
      cin >> a >> b >> f;
      a--; b--;
      dis[a][b] = f;
      dis[b][a] = f;
    }

    dfs(s-1,c,0);
    int ans = (1<<29);
    for(int i =0; i < c; i++){
      ans = min(ans, next[d-1][i]);
    }
    cout << ans << endl;
  }


}