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 <stdio.h>
#include <cctype>
#include <limits.h>
#include <math.h>
#include <complex>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <cstring>
#include <string>
#include <sstream>
#include <algorithm>
#include <iomanip>
#include <iostream>

#define VARIABLE(x) cerr << #x << "=" << x << endl
#define BINARY(x) static_cast<bitset<16> >(x);
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define REP(i,m,n) for (int i=m;i<(int)(n);i++)
#define if_range(x, y, w, h) if (0<=(int)(x) && (int)(x)<(int)(w) && 0<=(int)(y) && (int)(y)<(int)(h))

const int INF = 1e9;
const double EPS = 1e-8;
const double PI = 3.14159;
int dx[4]={0, 1, 0, -1}, dy[4]={-1, 0, 1, 0};
using namespace std;
typedef long long ll;
//typedef pair<int, int> P;
struct P {
	int x, y, n;
	P(int n, int x, int y):n(n), x(x), y(y){}
	P(){}
};

/** Problem0212 : Highway Express Bus **/
struct edge{
	int from, to, cost;
	edge(int f, int t, int c):from(f), to(t), cost(c){}
	edge(){}
};
vector<edge> G;

int main()
{
	int C, N, M, S, D;
	while (cin>>C>>N>>M>>S>>D, C) {
		S--, D--;
		G.clear();
		
		rep(i, M) {
			int a, b, f;
			cin>>a>>b>>f;
			a--, b--;
			G.push_back(edge(a, b, f));
			G.push_back(edge(b, a, f));
		}
		
		int d[100][11];
		fill(d[0], d[0]+1000, INF);
		for (int i=0; i<C+1; i++) d[S][i]=0;
		
		while (true) {
			bool update=false;
			
			for (int i=0; i<G.size(); i++) {
				edge e = G[i];
				for (int j=0; j<C+1; j++) {
					if (d[e.to][j] > d[e.from][j] + e.cost) {
						d[e.to][j] = d[e.from][j] + e.cost;
						update = true;
					}
					
					
					if (j+1<=C) {
						if (d[e.to][j+1] > d[e.from][j]+e.cost/2) {
							d[e.to][j+1] = d[e.from][j]+e.cost/2;
							update = true;
						}
					}
				}
			}
			
			if (!update) break;
		}
		
		int ans = INF;
		for (int i=0; i<C+1; i++) {
			ans = min(ans, d[D][i]);
		}
		cout << ans << endl;
	}
}

C++: #include<iostream>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;
#define INF (1<<24)

struct state{
  int cost,pos,cnt;
  bool operator < (const state &p) const{
    return cost>p.cost;
  }
};

struct edge{
  int to,cost;
};

int c,n,m,s,d;
vector<edge> G[100];

void init(){
  for(int i=0;i<100;i++)G[i].clear();
}

int dijkstra(int si,int ti){
  int d[100][11];
  for(int i=0;i<100;i++)
    for(int j=0;j<11;j++)d[i][j]=INF;

  d[si][c]=0;
  priority_queue< state > Q;
  Q.push((state){0,si,c});

  while(!Q.empty()){
    state s=Q.top();Q.pop();
    if(s.cost>d[s.pos][s.cnt])continue;

    for(int i=0;i<(int)G[s.pos].size();i++){
      edge e=G[s.pos][i];
      if(s.cost+e.cost>=d[e.to][s.cnt])continue;
      d[e.to][s.cnt]=s.cost+e.cost;
      Q.push((state){s.cost+e.cost,e.to,s.cnt});
    }

    if(s.cnt==0)continue;

    for(int i=0;i<(int)G[s.pos].size();i++){
      edge e=G[s.pos][i];
      if(s.cost+e.cost/2>=d[e.to][s.cnt-1])continue;
      d[e.to][s.cnt-1]=s.cost+e.cost/2;
      Q.push((state){s.cost+e.cost/2,e.to,s.cnt-1});
    }
  }//while

  int res=INF;
  for(int i=0;i<=c;i++){
    res=min(res,d[ti][i]);
  }
  return res;
}

int main(){
  int a,b,f;
  while(cin>>c>>n>>m>>s>>d){
    if(n==0)break;
    init();
    for(int i=0;i<m;i++){
      cin>>a>>b>>f;
      a--;b--;
      G[a].push_back((edge){b,f});
      G[b].push_back((edge){a,f});
    }
    cout<<dijkstra(s-1,d-1)<<endl;
  }
  return 0;
}