暴力：

class BlackBox {
    int cnt;
    boolean state[];
    int open=0;
    int A[];
    int B[];
    public BlackBox(int n, int m) {
        cnt=2*(m+n);
        state=new boolean[cnt];
        A=new int[cnt];//positive,negtive
        B=new int[cnt];//positive,negtive

        for(int i=0;i<A.length;i++){
            A[i]=(cnt-i)%cnt;//observation:because sum is total
            B[i]= (m*2-i+cnt) % cnt;
        }

    }
    
    public int open(int index, int direction) {
        if(!state[index]){
            state[index]=true;
            open++;
        }
        if(open==1)return index;

        do{
            if(direction==1){
                index=A[index];
            }else{
                index=B[index];
            }
            if(state[index])break;
            direction*=-1;
        }while(!state[index]);
        return index;
    }
    
    public void close(int index) {
        state[index]=false;
        open--;
    }
}

/**
 * Your BlackBox object will be instantiated and called as such:
 * BlackBox obj = new BlackBox(n, m);
 * int param_1 = obj.open(index,direction);
 * obj.close(index);
 */
 
 
 treemap 找循环解法
 
 
 
 class BlackBox {
    int cnt;
    int A[];int B[];
    int group=0;
    Map<String,Integer>map=new HashMap<>();
    Map<String,Integer>pos=new HashMap<>();
    TreeMap<Integer,Integer>treemaps[];
    public BlackBox(int n, int m) {
        cnt=2*(m+n);
        
        A=new int[cnt];//positive,negtive
        B=new int[cnt];//positive,negtive

        for(int i=0;i<A.length;i++){
            A[i]=(cnt-i)%cnt;//observation:because sum is total
            B[i]= (m*2-i+cnt) % cnt;
        }

        for(int i=0;i<cnt;i++){
            if(!map.containsKey(i+",1")){
                circle(i,1);
            }
            if(!map.containsKey(i+",-1")){
                circle(i,-1);
            }
        }
        treemaps=new TreeMap[group+1];
        for(int i=0;i<treemaps.length;i++){
            treemaps[i]=new TreeMap<>();
        }
    }
    
    public void circle(int index,int dir){
        Set<String>set=new HashSet<>();
        int start=index;
        int i=0;
        while(true){
            String state=index+","+dir;
            if(set.contains(state))break;
            
            map.put(state,group);
            pos.put(state,i++);
            set.add(state);
            if(dir==1){
                index=A[index];
            }else{
                index=B[index];
            }
            dir*=-1;
        }
        group++;
    }


    public int open(int index, int direction) {
        String state1=index+","+direction;
        String state2=index+","+-direction;

        int id1=map.get(state1);
        int val1=pos.get(state1);

        int id2=map.get(state2);
        int val2=pos.get(state2);

        treemaps[id1].put(val1,index);
        treemaps[id2].put(val2,index);


        Integer ceil=treemaps[id1].ceilingKey(val1+1);
        if(ceil!=null){
            return treemaps[id1].get(ceil);
        }

        ceil=treemaps[id1].ceilingKey(-1);
        return treemaps[id1].get(ceil);
    }
    
    public void close(int index) {
        String a=index+",-1";
        String b=index+",1";
        
        int id1=map.get(a);
        int id2=map.get(b);

        int v1=pos.get(a);
        int v2=pos.get(b);

        if(treemaps[id1].containsKey(v1))treemaps[id1].remove(v1);
        if(treemaps[id2].containsKey(v2))treemaps[id2].remove(v2);
    }
}

/**
 * Your BlackBox object will be instantiated and called as such:
 * BlackBox obj = new BlackBox(n, m);
 * int param_1 = obj.open(index,direction);
 * obj.close(index);
 */