1 /*
 2     Name: hdu--1104--Remainder
 3     Copyright: 版权2017 日天大帝
 4     Author: 日天大帝
 5     Date: 22/04/17 09:11
 6     Description: bfs
 7                 a = b * q + r (q > 0 and 0 <= r < q),
 8                 题上的取余运算和%运算不一样，%运算能产生负值所以要 （n%k+k)%k这样，才等于题意的取余
 9                 这个题用vis标记产生过的数据，同时用%km和%k进行剪枝优化 
10                  
11 */
12 #include<cstring>
13 #include<iostream>
14 #include<queue>
15 #include<string> 
16 using namespace std;
17 struct node{
18     int num,steps;
19     string str;
20 };
21 const int MAX = 1005;
22 bool vis[MAX];
23 int n,m,k,mk,final_cmp;
24 void bfs(){
25     node start;
26     start.num = n;
27     start.str = "";
28     start.steps = 0;
29     vis[(n%k+k)%k] = 1;
30     queue<node> q;
31     q.push(start);
32     
33     while(!q.empty()){
34         node a,temp = q.front();q.pop();
35         if(final_cmp == ((temp.num%k)+k)%k){
36             cout<<temp.steps<<endl<<temp.str<<endl;
37             return ;
38         }
39         for(int i=0; i<4; ++i){
40             a = temp;
41             if(i == 0){
42                 a.num += m;
43                 a.str += ‘+‘;
44             }else if(i == 1){
45                 a.num -= m;
46                 a.str += ‘-‘ ;
47             }else if(i == 2){
48                 a.num *= m;
49                 a.str += ‘*‘;
50             }else{
51                 a.num = (a.num%m+m)%m;
52                 a.str += ‘%‘ ;
53             }
54             a.num %= mk;//%k之后%m结果就错啦，10%(15) !=10%3%5
55             if(vis[(a.num%k+k)%k])continue;//%k缩小范围剪枝 
56             a.steps++;
57             vis[(a.num%k+k)%k] = 1;
58             q.push(a);
59         }
60     }
61     cout<<"0"<<endl;
62 }
63 int main(){
64     ios::sync_with_stdio(false);
65     
66     while(cin>>n>>k>>m,n||m||k){//输入有正负不能用n+m+k 
67         memset(vis,0,sizeof(vis));
68         mk = m*k;
69         final_cmp = ((n+1)%k+k)%k;
70         bfs() ;
71     }
72     return 0;
73 }