Go: package main

import (
	"container/heap"
	"fmt"
)

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
}

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)
		}
		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)
		start := Node{NowPosition: s, DiscountTicketTCount: c, Amount: 0}
		heap.Push(&pq, &start)
		for len(pq) != 0 {
			now := heap.Pop(&pq).(*Node)
			if now.NowPosition == d {
				fmt.Println(now.Amount)
				break
			}
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				heap.Push(&pq, next)
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					heap.Push(&pq, next)
				}
			}
		}
	}
}

C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <utility>
#include <tuple>
#include <queue>

#define REP(i, a, b) for (int i = int(a); i < int(b); i++)
#ifdef _DEBUG_
#define dump(val) cerr << __LINE__ << ":\t" << #val << " = " << (val) << endl
#else
#define dump(val)
#endif

using namespace std;

typedef long long int ll;
typedef tuple<int, int> P;
typedef tuple<ll, int, int> T;

template<typename T>
vector<T> make_v(size_t a, T b) {
    return vector<T>(a, b);
}

template<typename... Ts>
auto make_v(size_t a, Ts... ts) {
    return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}

template<typename T>
void chmin(T &a, T b) {
    a = min(a, b);
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int c, n, m, s, t;
    while (cin >> c >> n >> m >> s >> t, c + n + m + s + t) {
        s--;
        t--;
        vector<vector<P>> G(n);
        REP(i, 0, m) {
            int a, b, f;
            cin >> a >> b >> f;
            a--;
            b--;
            G[a].push_back({b, f});
            G[b].push_back({a, f});
        }
        const ll inf = 1LL << 60;
        auto dist = make_v(n, c + 1, inf);
        priority_queue<T, vector<T>, greater<T>> pq;
        // cost, ticket, vertex
        pq.emplace(0LL, c, s);
        REP(i, 0, c + 1) {
            dist[s][i] = 0;
        }
        while (pq.size()) {
            ll cost;
            int ticket, vertex;
            tie(cost, ticket, vertex) = pq.top();
            pq.pop();
            if (dist[vertex][ticket] < cost) continue;
            dist[vertex][ticket] = cost;
            for (auto p : G[vertex]) {
                int to, f;
                tie(to, f) = p;
                // use ticket
                if (ticket > 0 && dist[to][ticket - 1] > cost + f / 2) {
                    dist[to][ticket - 1] = cost + f / 2;
                    pq.emplace(dist[to][ticket - 1], ticket - 1, to);
                }
                // do not use ticket
                if (dist[to][ticket] > cost + f) {
                    dist[to][ticket] = cost + f;
                    pq.emplace(dist[to][ticket], ticket, to);
                }
            }
        }
        ll ans = inf;
        REP (i, 0, c + 1) {
            chmin(ans, dist[t][i]);
        }
        cout << ans << endl;
    }

    return 0;
}

C++: /*
g£_CNXg
*/
#include<iostream>
#include<queue>
#include<map>
#define INF 100000000
#include<vector>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
typedef pair<int,int> p;
typedef pair<int,p> P;
//P(cost,p(node,ticket))
struct edge{
	int cost,to;
};
int nticket,nnode,nedge,start,goal,d[11][101];
vector<edge> v[101];
void dijkstra(){
	int nowticket,nowplace,nowsum;
	priority_queue<P,vector<P>,greater<P> > que;
	que.push(P(0,p(start,nticket)));
	while(!que.empty()){
		P now=que.top();
		que.pop();
		
		nowsum=now.first;
		nowplace=now.second.first;
		nowticket=now.second.second;
		
		if(d[nowticket][nowplace]<nowsum)
			continue;
		rep(i,(int)v[nowplace].size()){
			edge e=v[nowplace][i];
			if(nowticket>0&&d[nowticket-1][e.to]>e.cost/2+nowsum){
				d[nowticket-1][e.to]=e.cost/2+nowsum;
				que.push(P(d[nowticket-1][e.to],p(e.to,nowticket-1)));
			}
			if(d[nowticket][e.to]>e.cost+nowsum){
				d[nowticket][e.to]=e.cost+nowsum;
				que.push(P(d[nowticket][e.to],p(e.to,nowticket)));
			}
		}
	}
}
void input(){
	int a,b,f;
	rep(i,nedge){
			cin>>a>>b>>f;
			a--;b--;
			edge c;
			c.cost=f;
			c.to=b;v[a].push_back(c);
			c.to=a;v[b].push_back(c);
		}
}
void init(){
	rep(i,nticket+1)
		rep(j,nnode){
			if(j==start)
			d[i][j]=0;
			else
			d[i][j]=INF;
	}
}
int main(){
	//d[ticket][node]=Å­ïp
	while(cin>>nticket>>nnode>>nedge>>start>>goal,nticket||nnode||nedge||start||goal){
		start--;goal--;
		//ticket:`Pbg
		//nnode:nodeÌ
		//nedge:edgeÌ
		//start¨goal
		input();
		init();
		dijkstra();
		int ans=INF;
		for(int i=0;i<nticket+1;i++)
		if(ans>d[i][goal])
		ans=d[i][goal];
		cout<<ans<<endl;
		for(int i=0;i<nedge;i++)
		v[i].clear();
	}
	return 0;
}

C++: #include <iostream>
#include <queue>
#include <cstring>
using namespace std;
int c, n, m, s, d;

int field[101][101];
int visited[11][101];

int main () {
	while (cin >> c >> n >> m >> s >> d, c || n || m || s || d) {
		memset(field, 0, sizeof(field));
		memset(visited, 0, sizeof(visited));
		for (int i = 0; i < m; i++) {
			int a, b, f;
			cin >> a >> b >> f;
			field[a][b] = field[b][a] = f / 10;
		}
		priority_queue<pair<int, pair<int, int> >, vector<pair<int, pair<int, int> > >, greater<pair<int, pair<int, int> > > > q;
		q.push(make_pair(0, make_pair(c, s)));
		while (!q.empty()) {
			pair<int, pair<int, int> > current = q.top();
			q.pop();
			if (current.second.second == d) {
				cout << current.first * 10 << endl;
				break;
			}
			visited[current.second.first][current.second.second] = 1;
			for (int i = 1; i <= n; i++) {
				if (field[current.second.second][i] > 0) {
					if (!visited[current.second.first][i]) {
						q.push(make_pair(current.first + field[current.second.second][i], make_pair(current.second.first, i)));
					}
					if (current.second.first > 0 && !visited[current.second.first - 1][i]) {
						q.push(make_pair(current.first + field[current.second.second][i] / 2, make_pair(current.second.first - 1, i)));
					}
				}
			}
		}
	}
	return 0;
}