#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <vector>
#include <ctype.h>

char line[10240];
int main()
{
    int M,N;
    int s, e,i,j;
    int *sumbuf;
    char *endp, *startp;
    printf("Please input M:");
    scanf("%d",&M);
    if(M<1){
         fprintf(stderr,"M should be no less than 1\n");
         return -1;
    }
    printf("Please input lowerbound of N:");
    scanf("%d",&s);
    printf("Please input upperbound of N:");
    scanf("%d",&e);
    if(s>e||s<1){
         fprintf(stderr,"s=%d, e=%d is out of range\n",s,e);
         return -1;
    }
    printf("Please input prefix pattern:");
start:
    gets(line);
    std::vector<int> d;
    startp=line;
    while(startp!=NULL){
        while(*startp!='\0'&&(isspace(*startp)||*startp==','))startp++;
        if(*startp=='\0')break;
        int x=(int)strtol(startp,&endp, 10);
        startp=endp;
        d.push_back(x);
    }
    if(d.size()==0){
       goto start;
    }
    if(d.size()*2>s){
        fprintf(stderr,"s=%d is too small for prefix size %d\n",s,(int)d.size());
        return -1;
    }
    if(d[0]!=0){
        fprintf(stderr,"The first number must b 0\n");
        return -1;
    }
    for(i=1;i<d.size();i++)if(d[i-1]>=d[i]){fprintf(stderr,"input pattern must be monotonic increasing\n");return -1;}
    int maxsize = (e-2*d.size()+1)*M+d[d.size()-1]*2+1;
    sumbuf=(int *)malloc(sizeof(int)*(2*maxsize+1));
    for(N=s;N<=e;N++){
        int cm = N-2*d.size()+1;
        int h = d[d.size()-1];
        int csize = cm*M+d[d.size()-1]*2;
        memset(sumbuf,0,sizeof(int)*(2*csize)+1);
        for(i=0;i<d.size();++i){
             for(j=0;j<=i;j++){
                 int v=d[i]+d[j];
                 sumbuf[v]++;sumbuf[2*csize-v]++;
                 v=d[j]-d[i];
                 sumbuf[csize+v]++;sumbuf[csize-v]++;
             }
        }
        for(i=0;i<d.size();++i){
             for(j=1;j<=cm;j++){
                 sumbuf[d[i]+h+M*j]++;
                 sumbuf[csize-d[i]+h+M*j]++;
             }
        }
        for(i=2;i<=2*cm;i++){
             sumbuf[2*h+M*i]++;
        }
        for(i=0;i<2*csize+1;i++){
             if(sumbuf[i]==0){
                 break;
             }
        }
        if(i<2*csize+1){
              printf("check failed for N=%d\n",N);
        }else{
              printf("check passed for N=%d\n",N);
              for(i=0;i<d.size();i++)printf("%d ",d[i]);
              for(i=0;i<cm;i++)printf("%d ",h+(i+1)*M);
              for(i=d.size()-2;i>=0;i--)printf("%d ",h+cm*M+h-d[i]);
              printf("\n");fflush(stdout);
        }
    }
}