#include using namespace std; using uint = unsigned int; using ll = long long; #define TYPE_OF( VAR ) remove_const::type >::type #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define CIN( LL , A ) LL A; cin >> A #define ASSERT( A , MIN , MAX ) assert( MIN <= A && A <= MAX ) #define CIN_ASSERT( A , MIN , MAX ) CIN( TYPE_OF( MAX ) , A ); ASSERT( A , MIN , MAX ) #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define QUIT return 0 #define RETURN( ANSWER ) cout << ( ANSWER ) << "\n"; QUIT #define RESIDUE( A , P ) ( A >= 0 ? A % P : P - ( - A - 1 ) % P - 1 ) #define POWER( ANSWER , ARGUMENT , EXPONENT , MODULO ) \ TYPE_OF( ARGUMENT ) ANSWER = 1; \ { \ TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT ); \ TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){ \ if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){ \ ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % MODULO; \ } \ ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % MODULO; \ EXPONENT_FOR_SQUARE_FOR_POWER /= 2; \ } \ } \ ll CheckBounded( const ll& A , const ll& N , const ll& bound ) { if( bound <= 1 ){ return -1; } if( N == 0 ){ return 1; } ll A_power = 1; ll exponent = 0; while( A_power < bound ){ A_power *= A; exponent++; } ll answer = CheckBounded( A , N - 1 , exponent ); if( answer != -1 ){ POWER( A_power_new , A , answer , bound ); answer = A_power_new; } return answer; } inline constexpr const ll bound_M = 2000; ll Solve( const ll& A , const ll& N , const ll& M ) { if( M == 1 ){ return 0; } else if( A == 1 || N == 0 ){ return 1; } ll A_power = 1; vector memory{}; memory.push_back( A_power ); uint memory_size = 1; uint period; bool searching = true; while( searching ){ A_power = ( A_power * A ) % M; FOR( i , 0 , memory_size ){ if( A_power == memory[i] ){ period = memory_size - i; searching = false; break; } } memory.push_back( A_power ); memory_size++; } ll answer = CheckBounded( A , N - 1 , bound_M ); if( answer == -1 ){ ll exponent = Solve( A , N - 1 , period ) - bound_M; exponent = RESIDUE( exponent , period ); POWER( tetration , A , bound_M + exponent , M ); answer = tetration; } else { POWER( tetration , A , answer , M ); answer = tetration; } return answer % M; } int main() { UNTIE; constexpr const ll bound = 1000000000; CIN_ASSERT( A , 1 , bound ); CIN_ASSERT( N , 0 , bound ); CIN_ASSERT( M , 1 , bound_M ); RETURN( Solve( A , N , M ) ); }