#include #define _overload(_1,_2,_3,name,...) name #define _rep(i,n) _range(i,0,n) #define _range(i,a,b) for(int i=int(a);i=int(b);--i) #define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__) using namespace std; const int limit=10000000; vector calc(int n){ vector ret(10,0); for(int i=2;i*i<=n;++i) while(n%i==0) ret[i%9]++,n/=i; if(n!=1) ret[n%9]++; return ret; } int power(int a,int n,int mod){ int b=1; while(n){ if(n&1) b=b*a%mod; a=a*a%mod; n>>=1; } return b; } const int t_limit=10000000; const int n_limit=10000000; int main(void){ int t=0,all=0; scanf("%d",&t); assert(1<=t&&t<=t_limit); rep(loop,t){ int n,x,a,b,m; scanf("%d %d %d %d %d",&n,&x,&a,&b,&m); assert(1<=n && n<=n_limit); assert(0<=x && x<=1e9); assert(0<=a && a<=1e9); assert(0<=b && b<=1e9); assert(1<=m && m<=1e9); all+=n; bool allzero=true; int ans=0,f[10]; fill(f,f+10,0); int num=n-1,den=1; rep(i,n){ int cur=x%10; x=((x^a)+b)%m; if(cur!=0) allzero=false; rep(j,10) cur=(cur*power(j,f[j],9))%9; ans=(ans+cur)%9; vector factor_num=calc(num),factor_den=calc(den); rep(j,10) f[j]+=factor_num[j]; rep(j,10) f[j]-=factor_den[j]; num--,den++; } if(allzero==false && ans==0) ans=9; printf("%d\n",ans); } assert(all<=n_limit); return 0; }