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 <iostream>
#include <queue>

#define INF 1e9

using namespace std;

struct Edge {
	int to, cost;
};
struct Node {
	int now, rest, cost;
};
bool operator <(const Node& n1, const Node& n2) {
	return n1.cost < n2.cost;
}
bool operator >(const Node& n1, const Node& n2) {
	return n1.cost > n2.cost;
}

int main() {
	int c, n, l, s, d;
	while ( cin >> c >> n >> l >> s >> d, c || n || l || s || d ) {
		--s, --d;

		vector<Edge> m[100];
		for (int i = 0; i < l; ++i) {
			int a, b, f; cin >> a >> b >> f; --a, --b;
			m[a].push_back( (Edge){ b, f } );
			m[b].push_back( (Edge){ a, f } );
		}

		int ans[100][11]; fill(&ans[0][0], &ans[0][0]+100*11, INF);
		priority_queue<Node, vector<Node>, greater<Node> > Q; Q.push( (Node){s, c, 0} );
		while ( !Q.empty() ) {
			Node node = Q.top(); Q.pop();
			if (node.cost >= ans[node.now][node.rest]) continue;
			ans[node.now][node.rest] = node.cost;

			for (int i = 0; i < m[node.now].size(); ++i) {
				Edge& e = m[node.now][i];
				if (node.cost+e.cost < ans[e.to][node.rest]) {
					Q.push( (Node){ e.to, node.rest, node.cost+e.cost } );
				}

				if (node.rest > 0) {
					if (node.cost+e.cost/2 < ans[e.to][node.rest-1]) {
						Q.push( (Node){ e.to, node.rest-1, node.cost+e.cost/2 } );
					}
				}
			}
		}
		int a = INF;
		for (int i = 0; i <= c; ++i) a = min(a, ans[d][i]);
		cout << a << endl;
	}
}

C++: #include<iostream>
#include<map>
#include<cstdio>
#include<vector>
#include<algorithm>
#include<queue>
using namespace std;
typedef pair< int,int> P;
typedef pair< int , P > road;
main(){
  while(1){
    int c,n,m,s,d;
    int a,b,f;
    vector< P > bus[120];
    int min_cost[120][12];
    queue< road > que;
    road r;
    P p;
    cin>>c>>n>>m>>s>>d;//c waribiki n mati m rosen s start d goal
    if(c==0&&n==0&&m==0&&s==0&&d==0)break;
    for(int i=1;i<=n;i++){
      for(int j=0;j<=c;j++){
	min_cost[i][j]=1<<21;
      }
    }
    for(int i=0;i<m;i++){
      cin>>a>>b>>f;
      p.first=b;
      p.second=f;
      bus[a].push_back(p);
      p.first=a;
      p.second=f;
      bus[b].push_back(p);
    }
    r.first=c;
    r.second.first=s;
    r.second.second=0;
    que.push(r);
    while(!que.empty()){
      road now=que.front();
      int size=bus[now.second.first].size();
      for(int i=0;i<size;i++){
	if(bus[now.second.first][i].second+now.second.second<min_cost[bus[now.second.first][i].first][now.first]){
	  min_cost[bus[now.second.first][i].first][now.first]=bus[now.second.first][i].second+now.second.second;
	  r.first=now.first;
	  r.second.first=bus[now.second.first][i].first;
	  r.second.second=bus[now.second.first][i].second+now.second.second;
	  que.push(r);
	}
	if(now.first!=0&&bus[now.second.first][i].second/2+now.second.second<min_cost[bus[now.second.first][i].first][now.first-1]){
	  min_cost[bus[now.second.first][i].first][now.first-1]=bus[now.second.first][i].second/2+now.second.second;
	  r.first=now.first-1;
	  r.second.first=bus[now.second.first][i].first;
	  r.second.second=bus[now.second.first][i].second/2+now.second.second;
	  que.push(r); 
	}
      }  
      que.pop();
    }
    while(!que.empty()){
      que.pop();
    }
    int mins=1<<21;
    for(int i=0;i<c;i++){
      mins=min(mins,min_cost[d][i]);
    }
    cout<<mins<<endl;
  }
}

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 = 101;
const int MAX_C = 11;
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,m) 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,m) 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
}