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 <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 <complex>
#include <stack>
#include <queue>
#include <cstring>
#include <sstream>
#include <cassert>
using namespace std;
static const double EPS = 1e-5;
typedef long long ll;
typedef pair<int,int> PI;
typedef vector<int> vi;
#define rep(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
#define mp make_pair
#define pb push_back
#define F first
#define S second


int c,n,m,s,d;
typedef struct{
  int to,cost;
}edge;

vector<edge> V[11*100];


int dijkstra(int from,int to){
  from=(c+1)*from+c;
  bool used[n*(c+1)];
  memset(used,0,sizeof(used));
  int len[n*(c+1)];
  rep(i,n*(c+1))len[i]=1<<23;
  len[from]=0;

  priority_queue<PI,vector<PI>,greater<PI> > Q;
  Q.push(mp(0,from));
  while(!Q.empty()){
    int cost=Q.top().F,tfrom=Q.top().S;Q.pop();
    if(used[tfrom])continue;
    used[tfrom]=true;
    rep(i,V[tfrom].size()){
      int tto=V[tfrom][i].to,tcost=V[tfrom][i].cost;
      if(used[tto])continue;
      len[tto]=min(len[tfrom]+tcost,len[tto]);
      Q.push(mp(len[tto],tto));
    }
  }
/*
  rep(i,n){
    rep(j,c+1)printf("%6d",len[i*(c+1)+j]);
    cout<<endl;
  }
*/
  int ans=len[to*(c+1)];
  rep(i,c+1)ans=min(ans,len[to*(c+1)+i]);
  return ans;
}

main(){
  while(cin>>c>>n>>m>>s>>d,c|n|m|s|d){
    --s,--d;
    rep(i,n*(c+1))V[i].clear();

    rep(j,m){
      int a,b,cost;
      cin>>a>>b>>cost;
      --a,--b;
      rep(i,c+1){
        V[a*(c+1)+i].pb((edge){b*(c+1)+i,cost});
        V[b*(c+1)+i].pb((edge){a*(c+1)+i,cost});
        if(i){
          V[a*(c+1)+i].pb((edge){b*(c+1)+i-1,cost/2});
          V[b*(c+1)+i].pb((edge){a*(c+1)+i-1,cost/2});
        }
      }
    }
/*
    rep(i,n*(c+1)){
      printf("%d ",i/(c+1)+1);
      rep(j,V[i].size()){
        printf("%d %6d ",V[i][j].to/(c+1)+1,V[i][j].cost);
      }
      cout<<endl;
    }
*/
    cout<<dijkstra(s,d)<<endl;
  }
}