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]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++: #include <algorithm>
#include <map>
#include <vector>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cstring>
#include <cctype>
#include <cstdlib>
#include <cmath>
#include <string>
#include <queue>
#include <stack>
#include <set>
using namespace std;

#define REP(i,n) for(int i=0; i<n; ++i)
#define IREP(it,array) for(vector<int>::iterator it=array.begin(); it!=array.end(); ++it)
#define SREP(it,array) for(vector<string>::iterator it=array.begin(); it!=array.end(); ++it)

#define MP       make_pair
#define PB       push_back
#define ALL(x)   (x).begin(),(x).end()

const int INF = 1<<29;
const double EPS = 1e-9;
double zero(double d){
  return d < EPS ? 0.0 : d;
}

typedef long long LL;
typedef pair<int,int> P;


int main()
{
  cout.setf(ios::fixed, ios::floatfield);
  cout.precision(7);

  int c,n,m,s,d;
  while( cin >> c >> n >> m >> s >> d , c ){

    int dis[11][101];
    bool used[11][101];
    int cost[101][101];

    REP(i,11){
      fill( dis[i], dis[i]+101, INF );
      fill( used[i], used[i]+101, false );
    }
    dis[0][s] = 0;

    REP(i,101){
      fill( cost[i], cost[i]+101, INF );
      //      cost[i][i] = 0;
    }

    REP(_t,m){
      int a,b,f;
      cin >> a >> b >> f;
      cost[a][b] = cost[b][a] = f;
    }


    while(true){

      // pick minimum distance in unused
      int mini=-1, minj=0;
      REP(i,c+1){
	REP(j,n+1){
	  if( ! used[i][j] ){
	    if( mini==-1 || dis[mini][minj] > dis[i][j] ){
	      mini = i;
	      minj = j;
	    }
	  }
	}
      }

      if( mini == -1)	break;
      used[mini][minj] = true;

      REP(i,m+1){
	dis[mini][i] = min( dis[mini][i], dis[mini][minj] + cost[minj][i] );
	if( mini + 1 <= c )
	  dis[mini+1][i] = min( dis[mini+1][i], dis[mini][minj] + cost[minj][i]/2 );	  
      }
    }

    int res=INF;
    REP(i,c+1)
      res = min( res, dis[i][d] );

    cout << res << endl;
  }

  return 0;
}

C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#define INF 1000000000;
#define dis first
#define mati second.first
#define sta  second.second
using namespace std;
typedef pair <int ,pair <int,int> > P;
vector <P> mp[101];
int c,n,m,start,goal;

int bit_count(int a) {
  a = (a & 0x55555555)+((a & 0xAAAAAAAA) >> 1 );
  a = (a & 0x33333333)+((a & 0xCCCCCCCC) >> 2 );
  a = (a & 0x0F0F0F0F)+((a & 0xF0F0F0F0) >> 4 );
  a = (a & 0x00FF00FF)+((a & 0xFF00FF00) >> 8 );
  a = (a & 0x0000FFFF)+((a & 0xFFFF0000) >> 16);
  return a;
}

void henkan(int n,int kai) {
  if(kai <= 10) {
    henkan(n/2,kai+1);  
  cout << n % 2 ;
  if(kai == 0) cout << endl;
  }
}

int dijkstra() {
  int flg[1025][102] = {},dis[1025][102];
  for(int j=0;j<1<<n;j++)
    for(int i=0;i<=n;i++) dis[j][i] = -INF;

  for(int j=1;j<1<<n;j++)flg[j][start] = 1;

  priority_queue <P> Q;
  P t;
  t.dis = 0, t.mati = start, t.sta = 0;
  Q.push(t);

  while(!Q.empty()) {
    t = Q.top(),Q.pop();
    if(flg[t.sta][t.mati] == 1) continue;
    flg[t.sta][t.mati] = 1;
    for(int i=0;i<mp[t.mati].size();i++){
      int ndis = mp[t.mati][i].dis;
      int nmati = mp[t.mati][i].mati;
      int nsta = t.sta | (1<<(nmati-1));
      P tt;
      if(dis[t.sta][nmati] < t.dis-ndis && flg[t.sta][nmati] == 0) {
	tt.dis = t.dis-ndis,tt.mati = nmati,tt.sta = t.sta;
	dis[t.sta][nmati] = t.dis-ndis;
	Q.push(tt);
      }
      if(bit_count(nsta)<= c&&dis[nsta][nmati]<t.dis-ndis/2 && flg[nsta][nmati]==0){
	tt.dis = t.dis - ndis/2 , tt.mati = nmati, tt.sta = nsta;
	dis[nsta][nmati] = t.dis-ndis/2;
	Q.push(tt);
      }
    }
  }

  int ans = -INF;
  for(int j=0;j<1<<n;j++)ans = max(ans,dis[j][goal]);
   
  return -ans;
}


int main() {

  while(1) {
    cin >> c >> n >> m >> start >> goal;
    if(c==0&&n==0&&m==0&&start==0&&goal==0) break;

    for(int i=0;i<=n;i++) mp[i].clear();
    for(int i=0;i<m;i++) {
      int a,b,f;
      cin >> a >> b >> f;
      P t;
      t.dis = f,  t.mati = b , t.sta = 0;
      mp[a].push_back(t);
      t.mati = a;
      mp[b].push_back(t);
    }

    cout << dijkstra() << endl;
  }

  return 0;
}