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
}

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)
					}
				}
			}
		}
	}
}

C++: #include "bits/stdc++.h"
using namespace std;
using ll = long long; using pii = pair<int, int>;
const int MOD = (int)1e9 + 7, INF = (1 << 27); const ll INFLL = (1LL << 55);
#define FOR(i,a,b) for(int (i)=(a);i<(int)(b);i++)
#define rep(i,n) FOR(i,0,n)
template<typename T> void dbg(T x) { cout << x << "\n"; }
template<typename T, typename U> static void chmin(T &x, U y) { if (y < x) x = y; }
template<typename T, typename U> static void chmax(T &x, U y) { if (x < y) x = y; }


int n, m;

// O(n^2)
using Dist = int;
const int VMAX = 110;
Dist cost[VMAX][VMAX];
Dist d[12][VMAX];
void dijkstra(int s, int a) {
    d[a][s] = 0;
    vector<int> used(n, 0);
    while (1) {
        int v = -1;
        for (int to = 0; to < n; to++) {
            if (used[to]) continue;
            if (v == -1 || d[a][to] < d[a][v]) v = to;
        }
        if (v == -1) break;
        used[v] = 1;
        for (int to = 0; to < n; to++) {
            Dist nd = d[a][v] + cost[v][to];
            if (a > 0) chmin(nd, d[a - 1][v] + cost[v][to] / 2);
            if (nd < d[a][to]) d[a][to] = nd;
        }
    }
}

void init() {
    fill_n(*d, 12 * VMAX, INF);
    fill_n(*cost, VMAX * VMAX, INF);
}

int main() {
    int c, s, t;
    while (cin >> c >> n >> m >> s >> t, c) {
        init();
        s--; t--;
        rep(i, m) {
            int a, b, f; cin >> a >> b >> f;
            a--; b--;
            cost[a][b] = cost[b][a] = f;
        }
        rep(a, c + 1) dijkstra(s, a);
        cout << d[c][t] << "\n";
    }

    return 0;
}

C++: //Solution for aoj:0212 Highway Express Bus
#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<functional>
using namespace std;
typedef pair<int, int>P;


struct S {
	int cost, to, num;
	S(int c, int t, int n) : cost(c), to(t), num(n){}
	bool operator>(const S &s) const {
		return cost > s.cost;
	}
};

const int INF = 1 << 30;
int c, n, m, s, d, ans;
int tocost[101][11];
vector<P> town[501];
priority_queue<S, vector<S>, greater<S> > pq;


void dijkstra(){
	while (!pq.empty()){
		S a = pq.top();
		pq.pop();
		for (int i = 0; i < town[a.to].size(); i++){
			int tt = town[a.to][i].first, cc = town[a.to][i].second;
			if (tocost[tt][a.num] > cc + a.cost){
				tocost[tt][a.num] = cc + a.cost;
				pq.push({ cc + a.cost, tt, a.num });
			}
			if (a.num&&tocost[tt][a.num-1] > cc/2 + a.cost){
				tocost[tt][a.num-1] = cc/2 + a.cost;
				pq.push({ cc/2 + a.cost, tt, a.num-1 });
			}
		}
	}
}
	int main(){
		while (cin >> c >> n >> m >> s >> d&&c){
			for (int i = 0; i < 101; i++)
				fill(tocost[i], tocost[i] + 11, INF);
			tocost[s][c] = 0;
			ans = INF;
			while (pq.size())
				pq.pop();
			for (int i = 0; i < n; i++)
					town[i].erase(town[i].begin(),town[i].end());
			for (int i = 0; i < m; i++){
				int a, b, c;
				cin >> a >> b >> c;
				town[a].push_back({ b, c });
				town[b].push_back({ a, c });
			}
			pq.push({ 0, s, c });
			dijkstra();
			for (int i = 0; i <= c; i++)
				ans = min(ans, tocost[d][i]);
			cout << ans << endl;
		}
		return 0;
	}

C++: #include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> P;
#define INF 1000000

int main() {
    while (true) {
        int c, n, m, s, d;
        cin >> c >> n >> m >> s >> d;
        
        if (c==0 && n==0 && m==0 && s==0 && d==0) {
            break;
        }
        
        s -= 1;
        d -= 1;
        
        vector<P> adj_list[n*(c+1)];
    
        for (int i=0; i<m; i++) {
            int ai, bi, fi;
            cin >> ai >> bi >> fi;
            ai -= 1;
            bi -= 1;
        
            for (int j=0; j<=c; j++) {
                adj_list[ai*(c+1)+j].push_back(P(bi*(c+1)+j, fi));
                adj_list[bi*(c+1)+j].push_back(P(ai*(c+1)+j, fi));
            
                if (j>0) {
                    adj_list[ai*(c+1)+j].push_back(P(bi*(c+1)+j-1, fi/2));
                    adj_list[bi*(c+1)+j].push_back(P(ai*(c+1)+j-1, fi/2));
                }
            }
        }
        
        priority_queue<P, vector<P>, greater<P>> pq;
        int dist[n*(c+1)];
        
        for (int i=0; i<n*(c+1); i++) {
            dist[i] = INF;
        }
        
        dist[s*(c+1)+c] = 0;
        pq.push(P(0, s*(c+1)+c));
        
        while (pq.size()) {
            P p = pq.top();
            pq.pop();
            
            int d = p.first;
            int v = p.second;
            
            if (dist[v]<d) {
                continue;
            }
            
            for (int i=0; i<adj_list[v].size(); i++) {
                int nv = adj_list[v][i].first;
                int w = adj_list[v][i].second;
                
                if (dist[nv]>dist[v]+w) {
                    dist[nv] = dist[v]+w;
                    pq.push(P(dist[nv], nv));
                }
            }
        }
        
        int ans = INF;
        
        for (int i=0; i<=c; i++) {
            ans = min(ans, dist[d*(c+1)+i]);
        }
        
        cout << ans << endl;
    }
}