Go: package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

var scanner = bufio.NewScanner(os.Stdin)

const INF = 0x7FFFFFFF

var pass [][]int

func main() {
	for scanner.Scan() {
		pass = make([][]int, 200)
		for i := range pass {
			pass[i] = make([]int, 200)
		}
		buf := strings.Split(scanner.Text(), " ")
		c, _ := strconv.Atoi(buf[0])
		n, _ := strconv.Atoi(buf[1])
		m, _ := strconv.Atoi(buf[2])
		s, _ := strconv.Atoi(buf[3])
		d, _ := strconv.Atoi(buf[4])
		if c == 0 && n == 0 && m == 0 && s == 0 && d == 0 {
			break
		}
		s--
		d--
		for i := 0; i < 200; i++ {
			for j := 0; j < 200; j++ {
				pass[i][j] = INF
			}
		}
		for i := 0; i < 200; i++ {
			pass[i][i] = 0
		}
		for i := 0; i < m; i++ {
			scanner.Scan()
			buf_ := strings.Split(scanner.Text(), " ")
			a, _ := strconv.Atoi(buf_[0])
			b, _ := strconv.Atoi(buf_[1])
			f, _ := strconv.Atoi(buf_[2])
			a--
			b--
			pass[a][b] = f
			pass[b][a] = f
		}
		fmt.Println(dijkstra(s, d, c, n))
	}
}

func dijkstra(s, g, c, n int) float64 {
	d := make([][]float64, 200)
	used := make([][]bool, 200)
	for i := 0; i < 200; i++ {
		d[i] = make([]float64, 20)
		used[i] = make([]bool, 20)
	}
	for i := range d {
		for j := range d[i] {
			d[i][j] = INF
		}
	}
	d[s][c] = 0
	for {
		v := -1
		w := -1
		for u := 0; u < n; u++ {
			for i := 0; i < c+1; i++ {
				if !used[u][i] && (v == -1 || d[u][i] < d[v][w]) {
					v = u
					w = i
				}
			}
		}
		if v == -1 {
			break
		}
		used[v][w] = true
		for u := 0; u < n; u++ {
			d[u][w] = math.Min(d[u][w], d[v][w]+float64(pass[v][u]))
			if w-1 >= 0 && pass[v][u] != INF {
				d[u][w-1] = math.Min(d[u][w-1], d[v][w]+(float64(pass[v][u]/2.0)))
			}
		}
	}
	ret := float64(INF)
	for i := 0; i < c+1; i++ {
		ret = math.Min(ret, d[g][i])
	}
	return ret
}

C++: #include <iostream>
#include <iomanip>
#include <sstream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <climits>
#include <cfloat>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
#include <algorithm>
#include <functional>
#include <utility>
#include <numeric>

using namespace std;

typedef unsigned int UI;
typedef long long LL;
typedef unsigned long long ULL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int,int> PII;
typedef istringstream ISS;
typedef ostringstream OSS;

#define REP( i, m, n ) for ( int i = (int)( m ); i < (int)( n ); ++i )
#define EACH( v, c ) for ( auto &v : c )

#define ITER( c ) __typeof( (c).begin() )
#define IREP( c, it ) for ( ITER(c) it = c.begin(); it != c.end(); ++it )
#define ALL( c ) (c).begin(), (c).end()

#define PB( n ) push_back( n )
#define MP( a, b ) make_pair( ( a ), ( b ) )
#define EXIST( c, e ) ( (c).find( e ) != (c).end() )

#define fst first
#define snd second

#define DUMP( x ) cerr << #x << " = " << ( x ) << endl
#define DEBUG( x ) cerr << __FILE__ << ":" << __LINE__ << ": " << #x << " = " << ( x ) << endl

struct Node
{
	int num, cost, tic;

	Node( int n, int c, int t ) : num( n ), cost( c ), tic( t )
	{
		return;
	}

	bool operator > ( const Node &a ) const
	{
		return cost > a.cost;
	}
};

struct Edge
{
	int to, cost;

	Edge( int t, int c ) : to( t ), cost( c )
	{
		return;
	}
};

int main()
{
	cin.tie( 0 );
	ios::sync_with_stdio( false );

	while ( true )
	{
		int c, n, m, s, d;
		cin >> c >> n >> m >> s >> d;

		if ( !( c | n | m | s | d ) )
		{
			break;
		}

		s--;
		d--;

		vector< vector< Edge > > G( n, vector< Edge >() );

		REP( i, 0, m )
		{
			int a, b, f;
			cin >> a >> b >> f;

			a--;
			b--;

			G[a].PB( Edge( b, f ) );
			G[b].PB( Edge( a, f ) );
		}

		VVI dist( n, VI( c + 1, INT_MAX ) );

		priority_queue< Node, vector< Node >, greater< Node > > que;
		que.push( Node( s, 0, 0 ) );

		while ( !que.empty() )
		{
			Node cur = que.top();
			que.pop();

			if ( c < cur.tic ||
				 dist[ cur.num ][ cur.tic ] < cur.cost )
			{
				continue;
			}

			dist[ cur.num ][ cur.tic ] = cur.cost;

			REP( i, 0, G[ cur.num ].size() )
			{
				que.push( Node( G[ cur.num ][i].to, cur.cost + G[ cur.num ][i].cost, cur.tic ) );
				que.push( Node( G[ cur.num ][i].to, cur.cost + G[ cur.num ][i].cost / 2, cur.tic + 1 ) );
			}
		}

		cout << dist[d][c] << endl;
	}

	return 0;
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define F first
#define S second
using namespace std;
typedef pair<int,int> P;// F -> to, S -> cost
typedef pair<P,int> PP;// F->P(to,cost), S->discount
int c,n,m,s,d;
vector<P> vec[1000]; // F -> pos , S -> cost
int MD[1000][13];
const int INF = 1<<29;

void dijkstra(){
  priority_queue<PP,vector<PP>,greater<PP> > que;
  rep(i,n+1)rep(j,13)MD[i][j] = INF;
  //syokika
  MD[s][c] = 0;
  que.push(PP(P(0,s),c));//dis,start,discount

  while(!que.empty() ){
    PP p = que.top();que.pop(); //priority_queのPPと
    int v = p.F.S;
    
    for(int i=0;i<vec[v].size();i++){
      P po = vec[v][i]; //vectorのPPは意味が違うので注意！！！
      //if(MD[v][po.S] < po.F.S)continue;
      if(MD[po.F][p.S] > p.F.F + po.S){
	MD[po.F][p.S] = p.F.F+po.S;
	que.push(PP(P(MD[po.F][p.S],po.F),p.S));
      }
      if(p.S > 0 && MD[po.F][p.S-1] > p.F.F + po.S/2 ){
	MD[po.F][p.S-1] = p.F.F+po.S/2;
	que.push(PP(P(MD[po.F][p.S-1],po.F),p.S-1));
   
      }
    }
  }
}


int main(){
  int x,y,co;
  while(true){
    cin >> c >> n >> m >> s >> d;
    if(c+n+m+s+d == 0)break;
    rep(i,1000)vec[i].clear();
    rep(i,m){
      cin >> x >> y >> co;
      vec[x].push_back(P(y,co));
      vec[y].push_back(P(x,co));
    }
    dijkstra();
    int ans = INF;
    for(int i=0;i<=c;i++){
      ans = min(ans,MD[d][i]);
    }
    cout << ans << endl;
  }
  return 0;
}

//Version.1

C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;

typedef pair<pair<int,int>,int> NODE;
#define cost first.first
#define ticket first.second
#define city second
#define make_bus_st(a,b,c) make_pair(make_pair(a,b),c)

int busMap[200][200] ;
int memo[200][20];

int main()
{
	int C, N, M, S, D;
	int a, b, f;
	
	while(cin >> C >> N >> M >> S >> D, C, N, M, S, D) {
		for(int i = 0; i < 200; i++) {
			for(int j = 0; j < 200; j++) {
				busMap[i][j] = 0;
				if(j < 20) { memo[i][j] = (1<<21); }
			}
		}
		
		vector<int> nextCity[200];
		
		for(int i = 0; i < M; i++) {
			cin >> a >> b >> f;
			busMap[a][b] = busMap[b][a] = f;
			nextCity[a].push_back(b);
			nextCity[b].push_back(a);
		}
		
		priority_queue<NODE> bus;
		bus.push(make_bus_st(0,C,S));
		
		while(!bus.empty()) {
			NODE tmp = bus.top();
			bus.pop();
			
			for(int i = 0; i < nextCity[tmp.city].size(); i++) {
				int next = nextCity[tmp.city][i];
				
				if((busMap[tmp.city][next] + tmp.cost) < memo[next][tmp.ticket]) {
					memo[next][tmp.ticket] = busMap[tmp.city][next] + tmp.cost;
					bus.push(make_bus_st(memo[next][tmp.ticket], tmp.ticket, next));
				}
				if(tmp.ticket && (((busMap[tmp.city][next] / 2) + tmp.cost) < memo[next][tmp.ticket-1])) {
					memo[next][tmp.ticket-1] = (busMap[tmp.city][next] / 2) + tmp.cost;
					bus.push(make_bus_st(memo[next][tmp.ticket-1], tmp.ticket-1, next));
				}
			}
		}
		
		int ans = (1<<21);
		for(int i = 0; i <= C; i++) {
			ans = min(ans, memo[D][i]);
		}
		cout << ans << endl;
	}
	
	
	return 0;
}