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]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)
					}
				}
			}
		}
		runtime.GC()
	}
}

C++: #include <stdio.h>
#include <string.h>
#include <algorithm>
#include <iostream>
#include <math.h>
#include <assert.h>
#include <vector>
#include <queue>

using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
static const double EPS = 1e-9;
static const double PI = acos(-1.0);

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define FOR(i, s, n) for (int i = (s); i < (int)(n); i++)
#define FOREQ(i, s, n) for (int i = (s); i <= (int)(n); i++)
#define FORIT(it, c) for (__typeof((c).begin())it = (c).begin(); it != (c).end(); it++)
#define MEMSET(v, h) memset((v), h, sizeof(v))

typedef int Weight;
struct Edge {
  int cnt;
  int src;
  int dest;
  Weight weight;
  Edge(int cnt, int src, int dest, Weight weight) : cnt(cnt), src(src), dest(dest), weight(weight) {;}
  bool operator<(const Edge &rhs) const {
    if (weight != rhs.weight) { return weight > rhs.weight; }
    return false;
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
typedef vector<Weight> Array;
typedef vector<Array> Matrix;

void PrintMatrix(const Matrix &matrix) {
  for (int y = 0; y < (int)matrix.size(); y++) {
    for (int x = 0; x < (int)matrix[y].size(); x++) {
      printf("%d ", matrix[y][x]);
    }
    puts("");
  }
}

int c, n, m, s, d;
bool visit[20][110];
int dist[20][110];

int main() {
  while (scanf("%d %d %d %d %d", &c, &n, &m, &s, &d), c|n|m|s|d) {
    MEMSET(visit, false);
    MEMSET(dist, 0x0f);
    s--; d--;
    Graph g(n);
    REP(i, m) {
      int f, t, cost;
      scanf("%d %d %d", &f, &t, &cost);
      f--; t--;
      g[f].push_back(Edge(0, f, t, cost));
      g[t].push_back(Edge(0, t, f, cost));
    }
    priority_queue<Edge> que;
    que.push(Edge(c, 0xdeadbeaf, s, 0));
    while (!que.empty()) {
      Edge e = que.top();
      que.pop();
      if (visit[e.cnt][e.dest]) { continue; }
      visit[e.cnt][e.dest] = true;
      if (e.dest == d) {
        printf("%d\n", e.weight);
        break;
      }
      FORIT(it, g[e.dest]) {
        if (e.cnt != 0) {
          int ncost = e.weight + it->weight / 2;
          if (ncost < dist[e.cnt - 1][it->dest]) {
            dist[e.cnt - 1][it->dest] = ncost;
            que.push(Edge(e.cnt - 1, 0xdeadbeaf, it->dest, ncost));
          }
        }
        int ncost = e.weight + it->weight;
        if (ncost < dist[e.cnt - 1][it->dest]) {
          dist[e.cnt][it->dest] = ncost;
          que.push(Edge(e.cnt, 0xdeadbeaf, it->dest, ncost));
        }
      }
    }
  }
}

C++: #include <iostream>
#include <algorithm>
#include <vector>
#include <queue>

using namespace std;

struct edge {
    int to, cost;
    edge() {}
    edge(int to_, int cost_): to(to_), cost(cost_) {}
};

struct state {
    int pos, cost;
    state (){}
    state (int pos_, int cost_): pos(pos_), cost(cost_) {}

    bool operator < (const state& o) const {
        return cost > o.cost;
    }
};

constexpr int INF = 1 << 29;

int C, M, N, S, D;

const int W = 100;
vector<edge> graph[1100];

int min_cost[1100];

bool solve() {
    cin >> C >> N >> M >> S >> D;
    if (C+N+M+S+D == 0) { return false; }
    --S; --D;

    for (int j = 0; j < M; ++j) {
        int a, b, f; cin >> a >> b >> f;
        --a; --b;
        for (int j = 0; j < C; ++j) {
            graph[a+j*W].emplace_back(b+j*W, f);
            graph[b+j*W].emplace_back(a+j*W, f);

            graph[a+j*W].emplace_back(b+(j+1)*W, f/2);
            graph[b+j*W].emplace_back(a+(j+1)*W, f/2);
        }
    }

    fill(min_cost, min_cost+1000, INF);
    min_cost[S] = 0;

    priority_queue<state, vector<state>> que;
    que.emplace(S, 0);

    while (!que.empty()) {
        state st = que.top(); que.pop();
        int pos = st.pos;
        int cost = st.cost;
        if (cost > min_cost[st.pos]) { continue; }

        for (edge& e : graph[pos]) {
            int next_cost = cost + e.cost;
            if (next_cost < min_cost[e.to]) {
                min_cost[e.to] = next_cost;
                que.emplace(e.to, next_cost);
            }
        }
    }

    int ans = INF;
    for (int j = 0; j <= C; ++j) {
        ans = min(ans, min_cost[D+j*W]);
    }
    cout << ans << endl;

    return true;
}

int main() {
    for (; solve(); ) ;
    return 0;
}