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 <bits/stdc++.h>
using namespace std;
#define FOR(i, s, n) for(int i = s; i < (int)n; i++)
#define per(i, n) for(int i = n; i >= 0; i--)
#define ROF(i, s, n) for(int i = s; i >= (int)n; i--)
#define FORIT(i, A) for (auto i : A)
#define PRINT(x) cout << (x) << "\n"
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define MP make_pair
#define EACH(i, n) for (__typeof((n).begin()) i = (n).begin(); i != (n).end(); ++i)
#define SZ(a) int((a).size())
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())
#define CLR(a) memset((a), 0 ,sizeof(a))
#define NCLR(a) memset((a), -1 ,sizeof(a))
#define dump(x) cout << #x << " = " << (x) << "\n";
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << "\n";
#define sq(n) (n) * (n)
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef priority_queue<int> maxpq;
typedef priority_queue< int, vector<int>, greater<int> > minpq;
static const double EPS = 1e-10;
static const double PI = acos( -1.0 );
static const int mod = 1000000007;
static const int INF = 1 << 30;
static const LL LL_INF = 1152921504606846976;
static const int dx[] = { -1, 0, 1, 0, 1, -1, 1, -1 };
static const int dy[] = { 0, -1, 0, 1, 1, 1, -1, -1 };



int c, n, m, s, d;
LL dp[ 100 ][ 101 ];
static LL _root[ 100 ][ 100 ];

LL solve( int now, int can_use, set<int> p ) {
	if ( now == d ) {
		return 0;
	}
	p.insert( now );
	if ( dp[ can_use ][ now ] >= 0 ) {
		return dp[ can_use ][ now ];
	}
	LL res = LL_INF;
	for ( int i = 0; i < n; ++i ) {
		if ( p.count( i ) || _root[ now ][ i ] >= res ) {
			continue;
		}
		res = min( res, solve( i, can_use, p ) + _root[ now ][ i ] );
		if ( can_use ) {
			res = min( res, solve( i, can_use - 1, p ) + _root[ now ][ i ] / 2 );
		}

	}
	return dp[ can_use ][ now ] = res;
}

int main() {
	while ( ~scanf( "%d %d %d %d %d", &c, &n, &m, &s, &d ) && n && m ) {
		--s;
		--d;
		for ( int i = 0; i < n; ++i ) {
			for ( int j = 0; j < n; ++j ) {
				_root[ i ][ j ] = LL_INF;
			}
			_root[ i ][ i ] = 0;
		}
		for ( int i = 0; i < m; ++i ) {
			int a, b, f;
			scanf( "%d %d %d", &a, &b, &f );
			--a;
			--b;
			_root[ a ][ b ] = _root[ b ][ a ] = min<LL>( _root[ a ][ b ], f );
		}
		NCLR( dp );
		LL ans = solve( s, c, set<int>() );
		printf( "%lld\n", ans );
	}
	return 0;
}

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

class Vertax
{
public:
	int n, d, c;
	Vertax(){}
	Vertax(int n, int d, int c) : n(n), d(d), c(c){}
};
bool operator > (Vertax v1, Vertax v2)
{
	if (v1.c == v2.c) return v1.d > v2.d;
	return v1.c > v2.c;
}
bool operator < (Vertax v1, Vertax v2)
{
	if (v1.c == v2.c) return v1.d < v2.d;
	return v1.c < v2.c;
}

typedef pair<int, int> p;
const int INF = 99999999;

int C, N, M, S, D; //??????????????°???????????°???????????°???????????°???????????°

int main()
{
	while (cin >> C >> N >> M >> S >> D, C + N + M + S + D)
	{
		vector<p> edge[101];
		priority_queue<Vertax, vector<Vertax>, greater<Vertax>> que;
		int distance[11][101];

		for (int i = 0; i < M; i++)
		{
			int a, b, f;
			cin >> a >> b >> f;
			edge[a].push_back(p(b, f));
			edge[b].push_back(p(a, f));
		}
		for (int i = 0; i <= C; i++)
		{
			for (int j = 0; j <= N; j++)
			{
				distance[i][j] = INF;
			}
		}
		
		Vertax start;
		start.n = S;
		start.d = 0;
		start.c = 0;
		que.push(start);
		distance[0][S] = 0;

		while (!que.empty())
		{
			int n = que.top().n;
			int d = que.top().d;
			int c = que.top().c;
			que.pop();

			for (int i = 0; i < edge[n].size(); i++)
			{
				int to = edge[n][i].first;
				int dis = edge[n][i].second;

				if (distance[c][to] > d + dis)
				{
					distance[c][to] = d + dis;
					que.push(Vertax(to, d + dis, c));
				}
				if (c < C && distance[c + 1][to] > d + (dis / 2))
				{
					distance[c + 1][to] = d + (dis / 2);
					que.push(Vertax(to, d + (dis / 2), c + 1));
				}
			}
		}

		int ans = INF;
		for (int i = 0; i <= C; i++)
		{
			ans = min(ans, distance[i][D]);
		}
		cout << ans << endl;
	}

	return 0;
}