/* ### # ############# # ####################### ################################ ######################################### ############################################## # ##################################### # ###### ############################ ###### ########### ################### # ########## ################ ######### ############### #################### # #################### ####### ############## ######################## ######## ######### ######################## ########### ####### ######################## ############## # ####### ######################## ######################## ######################## ######################## ######################## ######################## ######################## ###################### ####################### ################### ################### ############## ############### ########## ########## ###### ###### ## ## # # # # # # # # # # # #### #### #### #### #### # # # # # ## # # # # # # #____# ## # #/ # # ## # # # # # # # #^^^^ # ## ###/# # # # #### #### ###/# #### # # ## */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace { using Integer = __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; } class range{ long long start_, end_, step_; public: struct range_iterator{ long long val, step_; range_iterator(long long v, long long step) : val(v), step_(step) {} long long operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(long long len) : start_(0), end_(len), step_(1) {} range(long long start, long long end) : start_(start), end_(end), step_(1) {} range(long long start, long long end, long long step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } }; 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(); } string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; } } constexpr long long mod = 9_ten + 7; Integer power_mod(Integer x, Integer y, Integer mod){ Integer ret = 1; while(y){ if(y&1) ret = (ret*x) % mod; x = (x*x) % mod; y >>= 1; } return ret; } //find k such that x^k = y (mod z) //x and z are co-prime //x^(aH-b) = y (mod z) //x^aH = y * x^b (mod z) Integer baby_step_giant_step(Integer x, Integer y, long long z){ Integer H = sqrt(z) + 1; set> S; for(Integer i=0, w=y; ifirst == w){ return H * i - itr->second; } } return k; } Integer get_order(Integer a, Integer b){ return baby_step_giant_step(a, 1, b); } int main(){ string s; cin >> s; s += '^'; vector v(3, 0); for(int i=0, k=0; i<3; k++){ while(s[k] != '^'){ v[i] = v[i] * 10 + (s[k] - '0'); k++; } i++; } v[0] %= mod; if(v[0] == 0){ println(0,0); return 0; } if(v[0] == 1){ println(1,1); return 0; } Integer ord_a = get_order(v[0], mod); Integer ans_1 = my_pow_mod(v[0] % mod, v[1], mod); ans_1 = my_pow_mod(ans_1, v[2], mod); Integer ans_2 = my_pow_mod(v[0] % mod, my_pow_mod(v[1] % ord_a, v[2], ord_a), mod); println((long long)ans_1, (long long)ans_2); return 0; }