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 <algorithm>
#include <cmath>
#include <climits>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

using namespace std;

#define LOG(...) printf(__VA_ARGS__)
//#define LOG(...)
#define FOR(i,a,b) for(int i=(int)(a);i<(int)(b);++i)
#define REP(i,n) for(int i=0;i<(int)(n);++i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())
#define RSORT(c) sort((c).rbegin(),(c).rend())
#define CLR(a) memset((a), 0 ,sizeof(a))

typedef long long ll;
typedef unsigned long long ull;
typedef vector<bool> vb;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vb> vvb;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

#define INF 1e8

struct edge {
    int to, cost;
};

struct P {
    int from, cost, ticket;

    bool operator >(const P& p) const {
        return cost > p.cost;
    }
};

const int dx[] = {-1,0,1,0}; const int dy[] = {0,1,0,-1};

int ticket_n, node_n, edge_n, start, goal;

int main() {
    while (cin >> ticket_n >> node_n >> edge_n >> start >> goal, ticket_n|node_n|edge_n|start|goal) {
        vector<vector<edge>> E(node_n+1);
        REP(i, edge_n) {
            int from, to, cost;
            cin >> from >> to >> cost;
            E[from].push_back({to, cost});
            E[to].push_back({from, cost});
        }

        vvi G(edge_n+1, vi(ticket_n+1, INF));
        priority_queue<P, vector<P>, greater<P>> q;
        q.push({start, 0, ticket_n});
        while (!q.empty()) {
            P p = q.top(); q.pop();

            if (p.from == goal) {
                cout << p.cost << endl;
                break;
            }

            int from = p.from, cost = p.cost, ticket = p.ticket;
            for (edge e : E[from]) {
                // use ticket
                if (G[e.to][ticket] > cost + e.cost) {
                    G[e.to][ticket] = cost + e.cost;
                    q.push({e.to, cost + e.cost, ticket});
                }
                // don't use ticket
                if (ticket-1 >= 0) {
                    if (G[e.to][ticket-1] > cost + e.cost/2) {
                        G[e.to][ticket-1] = cost + e.cost/2;
                        q.push({e.to, cost + e.cost/2, ticket-1});
                    }
                }
            }
        }
    }
}

C++: #include <iostream>
#include <sstream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <algorithm>
#include <map>
#include <set>
#include <stack>
#include <vector>
#include <queue>
#include <bitset>
#include <string>
using namespace std;

#define REP(i,n) for(int i=0; i<n; i++)
#define RPA(i,s,e) for(int i=s; i<=e; i++)
#define RPD(i,s,e) for(int i=s; i>=e; i--)
#define PB(a) push_back(a)
#define MP(i,s) make_pair(i,s)
#define ALL(a) (a).begin(), (a).end()
#define PRT(a) cout << (a) << endl

typedef pair<int,int> P;

struct edge { int to, cost; };

const int INF = 1000000009;
const int MAX_V = 111;
const int MAX_C = 15;
vector<edge> G[MAX_V];

int c, n, m, s, d;
int p, q, r;
int dp[MAX_C][MAX_V];

void add_edge(int from, int to, int cost) {
	edge e1 = { to, cost };
	edge e2 = { from, cost };
	G[from].PB(e1);
	G[to].PB(e2);
}

void dijkstra(int f, int t, int k) {
	REP(j,n) dp[k][j] = INF;

	priority_queue<P, vector<P>, greater<P> > que;
	que.push(MP(0, f));
	dp[k][f] = 0;

	while(!que.empty()) {
		P p = que.top();
		que.pop();

		int v = p.second;
		REP(i,G[v].size()) {
			edge& e = G[v][i];
			int minval = dp[k][v] + e.cost;
			if(k > 0) minval = min(minval, dp[k-1][v] + e.cost / 2);
			if(dp[k][e.to] > minval) {
				dp[k][e.to] = minval;
				que.push(P(minval, e.to));
			}
		}
	}
}

void solve() {
	RPA(i,0,c) {
		dijkstra(s, d, i);
	}
	PRT(dp[c][d]);
}

void coding() {
	while(scanf("%d%d%d%d%d", &c, &n, &m, &s, &d) != EOF) {
		if(c == 0 && n == 0 && m == 0 && s == 0 && d == 0) break;

		s--; d--;
		REP(i,n) G[i].clear();

		REP(i,m) {
			scanf("%d%d%d", &p, &q, &r);
			p--; q--;
			add_edge(p, q, r);
		}
		solve();
	}
}

//#define _LOCAL_TEST

int main() {
#ifdef _LOCAL_TEST
	freopen("a.in", "r", stdin);
#endif

	coding();

#ifdef _LOCAL_TEST
	cout << endl;
	cout << "This is local test" << endl;
	cout << "Do not forget to comment out _LOCAL_TEST" << endl;
#endif
}