Go: package main

import (
	"container/heap"
	"fmt"
	"runtime"
)

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]struct{})
		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}] = struct{}{}
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if _, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok {
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if _, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok {
						heap.Push(&pq, next)
					}
				}
			}
		}
		runtime.GC()
	}
}

C++: #include <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <fstream>
#include <complex>
#include <stack>
#include <queue>

using namespace std;
typedef long long LL;
typedef pair<int, int> P;
static const double EPS = 1e-5;

#define FOR(i,k,n) for (int i=(k); i<(int)(n); ++i)
#define REP(i,n) FOR(i,0,n)
struct state{
  int pos,money,cic;
  state(int pos=0,int money=0,int cic=0):
    pos(pos), money(money), cic(cic) {}
};
struct edge{
  int to,cost;
  edge(int to=0,int cost=0):
    to(to),cost(cost) {}
};
bool operator < (const state& s, const state& t){
  return s.money > t.money;
}

int main(void){
  int c,n,m,s,d;
  while(cin>>c>>n>>m>>s>>d){
    if(c==0) break;
    s--;d--;
    vector< vector<edge> > graph(n);
    REP(i,m){
      int a,b,f;
      cin>>a>>b>>f;
      a--;b--;
      graph[a].push_back(edge(b,f));
      graph[b].push_back(edge(a,f));
    }
    priority_queue<state> que;
    que.push(state(s));
    bool used[110][20]={};
    while(!que.empty()){
      state nowstate = que.top(); que.pop();
      int pos = nowstate.pos;
      int money = nowstate.money;
      int cicket = nowstate.cic;
      if(pos == d){
        cout<<money<<endl;
        break;
      }
      if(used[pos][cicket])continue;
      used[pos][cicket] = true;
      REP(i,graph[pos].size()){
        edge e = graph[pos][i];
        que.push(state(e.to,money+e.cost,cicket));
        if(cicket != c) que.push(state(e.to,money+e.cost/2,cicket+1));
      }
    }
  }
  return 0;
}

C++: #include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <numeric>
using namespace std;

#define NONE -1

int c,n,m,s,d;
vector < vector <int> > P;
vector < vector <int> > E;
vector <int> R;
vector <bool> V;
int answer;

void solve( int t )
{
	if ( t == d )
	{
		sort( R.rbegin(), R.rend() );
		for ( int i = 0; i < min(c,(int)R.size()); i++ )
		{
			R[i] /= 2;
		}
		if ( answer == -1 )
			answer = accumulate( R.begin(), R.end(), 0 );
		else
			answer = min( answer, accumulate( R.begin(), R.end(), 0 ) );
	}
	else
	{
		V[t] = true;
		for ( vector <int>::iterator it = E[t].begin(); it != E[t].end(); it++ )
		{
			if ( V[*it] == false )
			{
				R.push_back( P[t][*it] );
				solve(*it);
				R.pop_back();
			}
		}
		V[t] = false;
	}
}

int main( void )
{
	while ( cin >> c >> n >> m >> s >> d && c && n && m && s && d )
	{
		s--;
		d--;
		P = vector < vector <int> >(n+1, vector <int>(n+1,NONE));
		E = vector < vector <int> >(n+1);
		for ( int i = 0; i < m; i++ )
		{
			int a, b, f;
			cin >> a >> b >> f;
			P[a-1][b-1] = f;
			P[b-1][a-1] = f;
			E[a-1].push_back( b-1 );
			E[b-1].push_back( a-1 );
		}

		R = vector <int>();
		V = vector <bool>(n+1,false);
		answer = -1;
		solve( s );
		cout << answer << endl;
	}

	return 0;
}

C++: #include <iostream>
#include <queue>
#include <climits>
#include <vector>
using namespace std;
typedef pair<pair<int,int>,int> NODE;
#define cost first.first
#define ticket first.second 
#define pos second
#define ppp(a,b,c) make_pair(make_pair(a,b),c)
#define rep(i,n) for(int i=0;i<n;i++)
#define INF (1<<21)

int info[100][100];
int n;

int dijk(int a,int b,int c){
	priority_queue<NODE,vector<NODE>,greater<NODE> >  Q;
	int memo[100][11];
	rep(i,100)rep(j,11)memo[i][j] = INF;
	rep(j,11)memo[a][j] = 0;
	
	Q.push(ppp(0,c,a));
	while( !Q.empty() ){
		NODE q = Q.top();Q.pop();
		for(int i=0;i<n;i++){
			if( info[q.pos][i]+q.cost < memo[i][q.ticket]){
				 memo[i][q.ticket] = info[q.pos][i]+q.cost;
				Q.push(ppp(info[q.pos][i]+q.cost ,q.ticket,i));
			}
			if( q.ticket && info[q.pos][i]/2+q.cost < memo[i][q.ticket-1] ){
					Q.push( ppp( info[q.pos][i]/2+q.cost , q.ticket-1, i));
				 memo[i][q.ticket-1] = info[q.pos][i]/2+q.cost;
			}
		}
	}
	int mi = (1<<21);
	rep(j,11)mi = min(memo[b][j],mi);
	return mi;
}
int main(){
	int c,m,s,d,a,b,f;
	while(cin >> c >> n >> m >> s >> d ,c ){
		s--;d--;
		rep(i,100)rep(j,100)info[i][j]=INF*2;
		
		for(int i=0;i<m;i++){
			cin >> a >> b >> f;
			a--;b--;
			info[a][b] = info[b][a] = f;
		}
		cout << dijk(s,d,c) << endl;
	}
}