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<stdio.h>
#include<string.h>
#include<utility>
#include<queue>
#include<algorithm>
using namespace std;
#define INF 100000000
int C,N,M,S,D,g1[101][101],g2[101][101],s,t,c,d[101],u[101];
typedef struct P{int p,c,t;}P;
struct Order
{
	bool operator ()(P const& a, P const& b) const
	{
		return a.c==b.c?a.t<b.t:a.c>b.c;
	}
};

P tmp,tmp2;
priority_queue<P,vector<P>,Order>Q;
int main()
{
	for(;scanf("%d%d%d%d%d",&C,&N,&M,&S,&D),C;)
	{
		for(int i=0;i<=N;i++)
		{
			d[i]=INF;
			for(int j=0;j<=N;j++)
				g1[i][j]=g2[i][j]=INF;
		}
		for(int i=0;i<N;i++)
		{
			scanf("%d%d%d",&s,&t,&c);
			g1[s][t]=g1[t][s]=c;
			g2[s][t]=g2[t][s]=c/2;
		}
		d[S]=0;
		tmp.c=0;tmp.p=S;tmp.t=C;
		Q.push(tmp);
		for(;!Q.empty();)
		{
			tmp=Q.top(),Q.pop();
			for(int i=1;i<=N;i++)
			{
				int nc=d[tmp.p]+g1[tmp.p][i];
				if((d[i]==nc&&u[i]>tmp.p)||d[i]>nc)
				{
					tmp2.c=d[i]=d[tmp.p]+g1[tmp.p][i];
					tmp2.p=i;
					tmp2.t=tmp.t;
					Q.push(tmp2);
				}
				nc=d[tmp.p]+g2[tmp.p][i];
				if(tmp.t>0&&((d[i]==nc&&u[i]>tmp.p-1)||d[i]>nc))
				{
					tmp2.c=d[i]=d[tmp.p]+g2[tmp.p][i];
					tmp2.p=i;
					tmp2.t=tmp.t-1;
					Q.push(tmp2);
				}
			}
		}
		printf("%d\n",d[D]);
	}
}

C++: #include <cstdio>
#include <queue>
#include <vector>
#include <utility>
#include <algorithm>
using namespace std;
typedef pair<int,int> _P;
typedef pair<int,_P> P;
int main() {
	int c,n,m,s,d;
	int a,b,f;
	int i,ans;
	int cost1[100][100],cost2[100][11];
	priority_queue<P,vector<P>,greater<P> > que;
	while(scanf("%d%d%d%d%d",&c,&n,&m,&s,&d),c) {
		fill(cost1[0],cost1[0]+100*100,1<<27);
		fill(cost2[0],cost2[0]+100*11,1<<27);
		for(i=0;i<m;i++) {
			scanf("%d%d%d",&a,&b,&f);
			cost1[a-1][b-1]=cost1[b-1][a-1]=min(cost1[a-1][b-1],f);
		}
		while(!que.empty()) que.pop();
		que.push(P(0,_P(s-1,0)));
		cost2[s-1][0]=0;
		while(!que.empty()) {
			P p=que.top();que.pop();
			if(cost2[p.second.first][p.second.second]<p.first) continue;
			for(i=0;i<n;i++) {
				if((p.first+cost1[p.second.first][i])<cost2[i][p.second.second]) {
					cost2[i][p.second.second]=p.first+cost1[p.second.first][i];
					que.push(P(cost2[i][p.second.second],_P(i,p.second.second)));
				}
				if(p.second.second+1<=c&&(p.first+cost1[p.second.first][i]/2)<cost2[i][p.second.second+1]) {
					cost2[i][p.second.second+1]=p.first+cost1[p.second.first][i]/2;
					que.push(P(cost2[i][p.second.second+1],_P(i,p.second.second+1)));
				}
			}
		}
		ans=(1<<27);
		for(i=0;i<=c;i++)ans=min(ans,cost2[d-1][i]);
		printf("%d\n",ans);
	}
}

C++: #include<iostream>
#include<cstdio>
#include<queue>
#include<vector>
#include<algorithm>

#define INF 1010000000
#define rep(i,n) for(int i=0;i<n;i++)
#define reps(i,n) for(int i=1;i<=n;i++)
#define sint(i) scanf("%d",&i);
#define sintt(i,j) scanf("%d%d",&i,&j);
#define sinttt(i,j,k) scanf("%d%d%d",&i,&j,&k);

using namespace std;

class S{
	public:
	int p;
	int v;
	int n;
	
	S(int p,int v,int n):p(p),v(v),n(n){}
	
	bool operator<(const S&a)const{
		return v>a.v;
		return v==a.v ? v>a.v : n <a.n;
	}
};

int main(){
	while(1){
		int c,n,m,s,g;
		scanf("%d%d%d%d%d",&c,&n,&m,&s,&g);
		if(c==0&&n==0&&m==0&&s==0&&g==0)break;
		
		int root[101][101];
		rep(i,101)rep(j,101)root[i][j]=INF;
		
		rep(i,101)root[i][i]=0;
		
		rep(i,m){
			int a,b,d;
			sinttt(a,b,d);
			root[a][b]=d;
			root[b][a]=d;
		}
		
		priority_queue<S> qui;
		qui.push(S(s,0,0));
		int ans=0;
		
		int visit[101][11];
		rep(i,101)rep(j,11)visit[i][j]=0;
		
		while(1){
			if(qui.empty()==1){
				ans=-1;
				break;
			}
			
			S u=qui.top();qui.pop();
			if(visit[u.p][u.n]==1){continue;}
			
			//printf("%d %d %d\n",u.p,u.v,u.n);
			if(u.p==g){
				ans=u.v;
				break;
			}
			
			visit[u.p][u.n]=1;
			
			reps(i,n){
				if(root[u.p][i]!=INF){
					if(visit[i][u.n]==0){
						qui.push(S(i,u.v+root[u.p][i],u.n));
					}
					if(visit[i][u.n+1]==0 && visit[u.p][u.n+1]==0 && u.n+1 <= c){
						qui.push(S(i,u.v+root[u.p][i]/2,u.n+1));
					}
				}
			}
		}
		printf("%d\n",ans);
	}
}

C++: #include <iostream>
#include <cstdio>
#include <cmath>
#include <vector>
#include <map>
#include <stack>
#include <queue>
#include <algorithm>
#include <set>

#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,j) FOR(i,0,j)

const int INF = 1 << 24;
const int dx[4] = {0, 0, 1, -1}, dy[4] = {1, -1, 0, 0};

typedef unsigned long long ull;

struct Edge{
    int to, cost;
};

int C, N, M, S, D;
std::vector<Edge> G[110];
int d[110][20], used[110][20];

void dijkstra(){
    REP(i, 110){
        REP(j, 20){
            d[i][j] = INF;
            used[i][j] = 0;
        }
    }

    d[S][0] = 0;

    while(1){
        int u = -1, v = -1;
        REP(i, N){
            REP(j, C){
                if(!used[i][j] && (u == -1 || d[u][v] > d[i][j])){u = i; v = j;}
            }
        }

        if(u == -1){break;}
        used[u][v] = 1;

        REP(i, G[u].size()){
            Edge &e = G[u][i];
            d[e.to][v+1] = std::min(d[e.to][v+1], d[u][v] + e.cost / 2);
            d[e.to][v] = std::min(d[e.to][v], d[u][v] + e.cost);
        }
    }
}

int main(){
    while(std::cin >> C >> N >> M >> S >> D, C){
        S--; D--;

        REP(i, 110){
            G[i].clear();
        }

        REP(i, M){
            int from, to, cost;
            std::cin >> from >> to >> cost;
            from--; to--;
        
            G[from].push_back({to, cost});
            G[to].push_back({from, cost});
        }

        dijkstra();

        int res = INF;
        REP(i, C+1){
            res = std::min(res, d[D][i]);
        }

        std::cout << res << std::endl;
    }
}