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 <string>
#include <sstream>
#include <algorithm>
#include <vector>
#include <utility>
#include <functional>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <deque>
 
using namespace std;
 
#define rep(i,n) REP(i,0,n)
#define REP(i,s,e) for(int i=(s); i<(int)(e); i++)
#define pb push_back
#define mp make_pair
#define all(r) r.begin(),r.end()
#define fi first
#define se second
#define println(X) cout<<X<<endl;
#define DBG(X) cout<<#X<<" : "<<X<<endl;
 
 
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vii;
typedef vector<ll> vl;
typedef vector<vl> vll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<int, pii> pp;

const int INF = 1e9;

double EPS = 1e-10;


int c, n, m, s, g;



const int MAX_V = 510;

int d[MAX_V][MAX_V][15];
int connect[MAX_V][MAX_V];
int V;
 
void warshall_floyd_init(){
	for(int i = 0; i < V; i++){
		for(int j = 0; j < V; j++){
			for(int k = 0; k <= c; k++){
				if(i == j) d[i][i][k] = 0;
				else d[i][j][k] = INF;
			}
			connect[i][j] = 0;
		}
	}
}

void warshall_floyd() {
				for(int l = c; l>=0; l--){
				//for(int l = 0; l <= c; l++){
	for (int k = 0; k < V; k++) {
		for (int i = 0; i < V; i++) {
			for (int j = 0; j < V; j++) {
					d[i][j][l] = min(d[i][j][l], d[i][k][l] + d[k][j][c]);
					if(l>0 && connect[k][j] > 0){
						d[i][j][l-1]=min(d[i][j][l-1], d[i][k][l]+connect[k][j]/2);
						//printf(" %d (%d -> %d), %d %d\n", l, );
					}
				}
			}
		}
	}
}
int main(){
	int a, b, f;
	int ans;
	while(cin>>c>>n>>m>>s>>g){
		if(c == 0 && n == 0 && m == 0 && s == 0 && g == 0) break;
		s--; g--;
		V = n;
		warshall_floyd_init();
		//cout<<d[0][2][0]<<endl;
		for(int i = 0; i < m; i++){
			cin>>a>>b>>f;
			//f/=10;
			a--; b--;
			//d[a][b][c] = d[b][a][c] = f;
			d[a][b][c] = min(d[a][b][c], f);
			d[b][a][c] = min(d[b][a][c], f);
			connect[a][b] = connect[b][a] = f;	
		}
		warshall_floyd();
		int ans = INF;
		for(int i = 0; i <= c; i++) ans = min(ans, d[s][g][i]);
		cout<<ans<<endl;
		//cout<<" "<<d[4][5][2]<<endl;
	}
	
}

C++: #include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iterator>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#include <fstream>
#include <iomanip>
#include <cassert>
//#include <utility>
//#include <memory>
//#include <functional>
//#include <deque>
//#include <cctype>
//#include <ctime>
//#include <numeric>
//#include <list>
//#include <iomanip>

//#if __cplusplus >= 201103L
//#include <array>
//#include <tuple>
//#include <initializer_list>
//#include <forward_list>
//
//#define cauto const auto&
//#else

//#endif

using namespace std;


typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<long long> vll, vLL;
typedef vector<vector<long long> > vvll, vvLL;

#define VV(T) vector<vector< T > >

template <class T>
void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()){
    v.assign(a, vector<T>(b, t));
}

template <class F, class T>
void convert(const F &f, T &t){
    stringstream ss;
    ss << f;
    ss >> t;
}

#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define reep(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) reep((i),0,(n))
#define ALL(v) (v).begin(),(v).end()
#define PB push_back
#define F first
#define S second
#define mkp make_pair
#define RALL(v) (v).rbegin(),(v).rend()
#define DEBUG
#ifdef DEBUG
#define dump(x)  cout << #x << " = " << (x) << endl;
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#else
#define dump(x) 
#define debug(x) 
#endif
#define LDcout(x,n) fixed<<setprecision(n)<<x

#define MOD 1000000007LL
#define EPS 1e-8
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
#define maxs(x,y) x=max(x,y)
#define mins(x,y) x=min(x,y)

int c,n,m,s,d;

VV(pii) vv;


void mainmain(){
	while(cin>>c>>n>>m>>s>>d,c){
		vv=VV(pii)(n);
		s--;
		d--;
		rep(i,m){
			int a,b,t;
			cin>>a>>b>>t;
			a--;
			b--;
			vv[a].PB(pii(b,t));
			vv[b].PB(pii(a,t));
		}
		vvint dp;
		initvv(dp,n,c+1,-1);
		typedef pair<int,pii> P;
		priority_queue<P> pq;
		pq.push(mkp(0,pii(0,s)));
		while(pq.size()){
			P top=pq.top();
			pq.pop();
			if(dp[top.S.S][-top.S.F]>=0) continue;
			dp[top.S.S][-top.S.F]=-top.F;
			for(auto x:vv[top.S.S]){
				if(dp[x.F][-top.S.F+1]<0){
					pq.push(mkp(top.F-x.S/2,pii(top.S.F-1,x.F)));
				}
				if(dp[x.F][-top.S.F]<0){
					pq.push(mkp(top.F-x.S,pii(top.S.F,x.F)));
				}
			}
		}
		int ans=INF;
		rep(i,c+1){
			mins(ans,dp[d][i]);
		}
		cout<<ans<<endl;
	}
}


signed main() {
	ios_base::sync_with_stdio(false);
    cin.tie(0);
  	cout<<fixed<<setprecision(20);
    mainmain();
}