#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace { using Integer = long long; //__int128; template istream& operator >> (istream& is, vector& vec){for(T& val: vec) is >> val; return is;} template istream& operator , (istream& is, T& val){ return is >> val;} template ostream& operator << (ostream& os, const vector& vec){for(int i=0; i ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template void print(const H& head){ cout << head; } template void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template void println(const T& ... values){ print(values...); cout << endl; } template void eprint(const H& head){ cerr << head; } template void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template void eprintln(const T& ... values){ eprint(values...); cerr << endl; } string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast(chrono::steady_clock::now().time_since_epoch()).count()); template string join(const vector& v, const string& sep){ stringstream ss; for(int i=0; i0) ss << sep; ss << v[i]; } return ss.str(); } } constexpr long long mod = 9_ten + 7; int main_(){ int t; cin >> t; vector p_two_m9 = {1,2,4,8,7,5}; // 2^k mod 9 vector convert = {0,0,1,0,2,5,0,4,3}; // x = 2^convert[x] in mod 9 while(t--){ long long n,r,a,b,m; scanf("%lld%lld%lld%lld%lld", &n,&r,&a,&b,&m); auto s = [&r,n,a,b,m](){ int ret = r; r = ((r^a)+b) % m; return ret%10; }; bool zero = true; int ans = 0; int cnt_three = 0; //3^cnt_three int cnt_two = 0; //2^cnt_two n--; for(int i=0; i<=n; i++){ int si = s(); if(si != 0) zero = false; { int val = i; while(val && val%3==0){ cnt_three--; val/=3; } val %= 9; cnt_two -= convert[val]; cnt_two = (cnt_two+6)%6; } int k = p_two_m9[ cnt_two%6 ] * my_pow_mod(3, min(2,cnt_three), 9) % 9; ans += si * k; if(ans >= 9) ans %= 9; { int val = (n-i); while(val && val%3==0){ cnt_three++; val/=3; } val %= 9; cnt_two += convert[val]; cnt_two = (cnt_two+6)%6; } } if(ans == 0 && !zero) ans = 9; printf("%lld\n", ans); } return 0; } template void get_process_time(T (*func)(Args...), const Args& ... a){ auto start_time = chrono::steady_clock::now(); func(a...); auto end_time = chrono::steady_clock::now(); eprintln("executed in", chrono::duration_cast(end_time-start_time).count(), " [ms]"); } int main(){ get_process_time(main_); return 0; }