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 <iostream>
#include <vector>
#include <queue>
using namespace std;

const int INF = 1 << 30;

class State
{
public:
  int v, c, f;
  State(int _v, int _c, int _f)
    :v(_v), c(_c), f(_f) {}
  bool operator < (const State& st) const
  {
    return this->f > st.f;
  }
};

int main()
{
  int c, n, m, s, d;
  while (cin >> c >> n >> m >> s >> d) {
    if ((c|n|m|s|d) == 0)
      break;

    --s;
    --d;
    vector<vector<int> > path(n, vector<int>(n, INF));
    for (int i = 0; i < m; ++i) {
      int a, b, f;
      cin >> a >> b >> f;
      --a;
      --b;
      path[a][b] = path[b][a] = f;
    }

    priority_queue<State> que;
    que.push(State(s, c, 0));
    vector<vector<int> > dp(n, vector<int>(c+1, INF));
    while (!que.empty()) {
      const State st = que.top();
      que.pop();

      if (st.v == d) {
	cout << st.f << endl;
	break;
      }

      if (dp[st.v][st.c] < st.f)
	continue;
      dp[st.v][st.c] = st.f;

      for (int i = 0; i < n; ++i) {
	if (path[st.v][i] == INF)
	  continue;

	if (st.c > 0) {
	  if (dp[i][st.c-1] > st.f + path[st.v][i]/2) {
	    dp[i][st.c-1] = st.f + path[st.v][i]/2;
	    que.push(State(i, st.c-1, dp[i][st.c-1]));
	  }
	}

	if (dp[i][st.c] > st.f + path[st.v][i]) {
	  dp[i][st.c] = st.f + path[st.v][i];
	  que.push(State(i, st.c, dp[i][st.c]));
	}
      }
    }

  }
  return 0;
}

C++: #include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define RFOR(i,a,b) for(int i=(b) - 1;i>=(a);i--)
#define REP(i,n) for(int i=0;i<(n);i++)
#define RREP(i,n) for(int i=n-1;i>=0;i--)

#define PB push_back
#define INF INT_MAX/3
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CLR(a) memset(a,0,sizeof(a))

typedef long long int ll;

using namespace std;

int c,n,m,s,d;
int rosen[101][101] = {-1};
int saiki(int p,vector<int> st,vector<bool> &u){
    int ans = INF;
    if(p == d){
	sort(RALL(st));
	int tc = min(c,(int)(st.size()));
	REP(i,tc){
	    st[i] /= 2;
	}
	int sum = 0;
	REP(i,st.size()){
	    sum += st[i];
	}
	return sum;
    }
    FOR(i,1,n+1){
	if(!u[i] && rosen[p][i] > 0){
	    vector<int> temp = st;
	    vector<bool> utemp = u;
	    temp.PB(rosen[p][i]);
	    utemp[i] = true;
	    ans = min(ans,saiki(i,temp,utemp));
	}
    }
    return ans;
}

int main(){
    while(true){
	scanf("%d%d%d%d%d",&c,&n,&m,&s,&d);
	if(c==0&&n==0&&m==0&&s==0&&d==0) break;
	memset(rosen,-1,sizeof(rosen));
	REP(i,m){
	    int a,b,f;
	    cin >> a >> b >> f;
	    rosen[a][b] = f;
	    rosen[b][a] = f;
	}
	vector<bool>  used(n+1,false);
	vector<int> nanika;
	used[s] = true;
	cout << saiki(s, nanika ,used) << endl;
    }
    return 0;
}

C++: #include<iostream>
#include<iomanip>
#include<math.h>
#include<algorithm>
#include<string>
#include<vector>
#include<queue>
#include<stack>
#include<set>
#include<map>
#define REP(i, N) for(ll i = 0; i < N; ++i)
#define FOR(i, a, b) for(ll i = a; i < b; ++i)
#define ALL(a) (a).begin(),(a).end()
#define pb push_back
#define INF (long long)1000000000
#define MOD 1000000007
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

int main(void) {
	while(true) {
		ll c, n, m, s, d;
		cin>>c>>n>>m>>s>>d;
		if(c == 0 && n == 0 && m == 0 && s == 0 && d == 0) break;
		--s;
		--d;
		vector<vector<P> > p(n);
		vector<vector<ll> > dir(n, vector<ll>(c + 1, INF * INF));
		REP(i, m) {
			int a, b, f;
			cin>>a>>b>>f;
			--a;
			--b;
			p[a].pb(P(b, f));
			p[b].pb(P(a, f));
		}
		priority_queue<pair<P, ll> > que;
		que.push(pair<P, ll>(P(0, s), c));
		dir[s][c] = 0;
		while(!que.empty()) {
			pair<P, ll> np = que.top();
			que.pop();
			if(dir[np.first.second][np.second] != np.first.first) continue;
			REP(i, p[np.first.second].size()) {
				if(dir[p[np.first.second][i].first][np.second] > dir[np.first.second][np.second] + p[np.first.second][i].second) {
					dir[p[np.first.second][i].first][np.second] = dir[np.first.second][np.second] + p[np.first.second][i].second;
					que.push(pair<P, ll>(P(dir[p[np.first.second][i].first][np.second], p[np.first.second][i].first), np.second));
				}
				if(np.second > 0 && dir[p[np.first.second][i].first][np.second - 1] > dir[np.first.second][np.second] + p[np.first.second][i].second / 2) {
					dir[p[np.first.second][i].first][np.second - 1] = dir[np.first.second][np.second] + p[np.first.second][i].second / 2;
					que.push(pair<P, ll>(P(dir[p[np.first.second][i].first][np.second - 1], p[np.first.second][i].first), np.second - 1));
				}
			}
		}
		ll res = INF * INF;
		REP(i, c + 1) {
			res = min(res, dir[d][i]);
		}
		cout<<res<<endl;
	}
}