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;

const double PI = acos(-1);
const double EPS = 1e-15;
using ll = long long;
using ull = unsigned long long;
const int inf = 2e9;
const ll INF = 2e18;
const ll MOD = 1e9+7;
const ll MOD1 = 998244353;
typedef pair<int,int> P;

#define REP(i,n) for (int i = 0; i < (n); i++)
#define sz(s) (s).size()
#define pb push_back
#define fi first
#define se second
#define mp make_pair

int main(){
  int c,n,m,s,d;
  while (cin >> c >> n >> m >> s >> d,c,n,m,s,d) {
    ll dp[110][11];
    REP(i,110) REP(j,11) dp[i][j] = inf;
    s--;
    d--;
    vector<pair<int,ll>> G[110];
    REP(i,m) {
      int a,b;
      ll f;
      cin >> a >> b >> f;
      a--;
      b--;
      G[a].pb({b,f});
      G[b].pb({a,f});
    }
    priority_queue<pair<ll,pair<int,int>>,vector<pair<ll,pair<int,int>>>,greater<pair<ll,pair<int,int>>>> pq;
    dp[s][0] = 0;
    pq.push({0,{s,0}});
    while (!pq.empty()) {
      pair<ll,pair<int,int>> tp = pq.top();
      //cout << tp.fi << " " << tp.se.fi << " " << tp.se.se << endl;
      pq.pop();
      int point = tp.se.fi;
      int ticket = tp.se.se;
      if (tp.fi > dp[point][ticket]) continue;
      //cout << "test" << endl;
      REP(i,sz(G[point])) {
        int next = G[point][i].fi;
        ll cost = G[point][i].se;
        if (dp[point][ticket] + cost < dp[next][ticket]) {
          dp[next][ticket] = dp[point][ticket] + cost;
          pq.push({dp[next][ticket],{next,ticket}});
        }
        if (dp[point][ticket] + cost/2 < dp[next][ticket+1]) {
          dp[next][ticket+1] = dp[point][ticket] + cost/2;
          pq.push({dp[next][ticket+1],{next,ticket+1}});
        }
      }
    }
    ll ans = inf;
    REP(i,c+1) {
      ans = min(ans,dp[n][i]);
    }
    cout << dp[d][c] << endl;
  }
  return 0;
}

C++: #include<bits/stdc++.h>
using namespace std;
#define INF (1<<29)//INF
#define F first
#define S second
#define VS vector<string>
#define VI vector<int>
#define REPI(i,s,n) for(int i=s;i<n;i++)//sからn未満の間iを回す
#define REPJ(j,s,n) for(int j=s;j<n;j++)//sからn未満の間iを回す
#define RREPI(i,s,n) for(int i=s;i>=n;i--)//sからn以下の間iを回す
#define RREPJ(j,s,n) for(int j=s;j>=n;j--)//sからn以下の間jを回す
#define ALL(a) a.begin(),a.end()//ソートとかに使える sort(ALL(vec))のように
#define SET(a,c) memset(a,c,sizeof(a));//aをc（0or1）で初期化する
#define DEBUGONE(x) cout<<#x<<" : "<<x<<endl;//デバックで一つの変数を表示
#define DEBUGTWO(x,y) cout<<#x<<" : "<<x<<" "<<#y<<" : "<<y<<endl;//デバックで二つの変数を表示
#define DEBUGTHREE(x,y,z) cout<<#x<<" : "<<x<<" "<<#y<<" : "<<y<<" "<<#z<<" : "<<z<<endl;//デバックで三つの変数を表示
#define OUTONE(x) cout<<x<<endl;//一つの変数を表示
#define OUTTWO(x,y) cout<<x<<" "<<y<<endl;//二つの変数を表示
#define OUTTHREE(x,y,z) cout<<x<<" "<<y<<" "<<z<<endl;//三つの変数を表示
typedef long long int64;
typedef pair<string,int> Psi;
typedef pair<int,int> Pii;
typedef pair<int,Pii> Ppii;
typedef struct{
  vector<Pii> to;
  int mins;
}Edge;
bool flag[105];
main(){
  int c,n,m,s,d;
  while(cin>>c>>n>>m>>s>>d,c||n||m||s||d){
    Edge edge[105];
    for(int i=1;i<=n;i++){
      edge[i].to.clear();
      flag[i]=true;
      edge[i].mins=INF;
    }
    REPI(i,0,m){
      int from,to,cost;
      cin>>from>>to>>cost;
      edge[from].to.push_back(Pii(to,cost));
      edge[to].to.push_back(Pii(from,cost));
    }
    priority_queue<Ppii,vector<Ppii>,greater<Ppii> > que;//F=cost,S.F=now,S.S=ticket
    que.push(Ppii(0,Pii(s,c)));
    while(!que.empty()){
      Ppii now=que.top();
      que.pop();
      int nowc=now.F,nowp=now.S.F,nowt=now.S.S;
      //DEBUGTHREE(nowc,nowp,nowt);
      if(nowp==d){
	OUTONE(nowc);
	break;
      }
      Edge nowe=edge[nowp];
      flag[nowp]=false;
      int size=nowe.to.size();
      REPI(i,0,size){
	int nextp=nowe.to[i].F;
	//DEBUGTWO(nowe.to[i].F,nowe.to[i].S);
	if(flag[nextp]==true&&edge[nextp].mins>nowc+edge[nowp].to[i].S){
	  //cout<<"A"<<endl;
	  edge[nextp].mins=nowc+edge[nowp].to[i].S;
	  que.push(Ppii(nowc+edge[nowp].to[i].S,Pii(nextp,nowt)));
	}
	if(nowt>0&&flag[nextp]==true&&edge[nextp].mins>nowc+(edge[nowp].to[i].S/2)){
	  //cout<<"B"<<endl;
	  edge[nextp].mins=nowc+(edge[nowp].to[i].S);
	  que.push(Ppii(nowc+(edge[nowp].to[i].S/2),Pii(nextp,nowt-1)));
	}
      }
    }
  }
}