#include #include #include #include using namespace std; using ll = long long; #define CIN( LL , A ) LL A; cin >> A #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( remove_const::type >::type VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT , 0 , HOW_MANY_TIMES ) #define QUIT return 0 #define RETURN( ANSWER ) cout << ( ANSWER ) << "\n"; QUIT #include #define MAIN main int MAIN() { CIN( ll , N ); constexpr const ll bound = ( ll( 1 ) << 29 ) + 1; assert( -bound < N && N < bound ); CIN( int , E ); assert( 0 <= E && E <= 13 ); if( N == 0 ){ RETURN( 0 ); } else if( N < 0 ){ N += 1220703125; } int vN = 0; while( N % 5 == 0 ){ N /= 5; vN++; } if( vN >= E ){ RETURN( 0 ); } else if( vN % 2 == 1 ){ RETURN( "NaN" ); } vN /= 2; int E_minus_vN_half = E - vN; ll five_power_E_minus_vN_half = 1; REPEAT( E_minus_vN_half ){ five_power_E_minus_vN_half *= 5; } int kN = 0; // mod 5^13 = 1220703125 での1の原始4乗根123327057を前準備で計算 ll zeta = 123327057 % five_power_E_minus_vN_half; while( N % 5 != 1 ){ N = ( N * zeta ) % five_power_E_minus_vN_half; kN++; } if( kN % 2 == 1 ){ RETURN( "NaN" ); } N--; // mod 5^13 = 1220703125 での5素成分の逆元を前準備で計算 constexpr const ll inverse[18] = { 0 , // ダミー 1 , 610351563 , 406901042 , 915527344 , 1 , 203450521 , 697544643 , 457763672 , 949435764 , 610351563 , 887784091 , 712076823 , 469501202 , 959123884 , 406901042 , 228881836 , 789866728 }; const ll& half = inverse[2]; ll r = 1; ll uN_minus_power = 1; ll product = 1; ll factorial = 1; ll five_power_i = 1; ll term; FOR( i , 1 , 18 ){ uN_minus_power = ( uN_minus_power * N ) % five_power_E_minus_vN_half; product = ( product * ( half + 1 - i ) ) % five_power_E_minus_vN_half; factorial = ( factorial * inverse[i] ) % five_power_E_minus_vN_half; if( i != 0 && i % 5 == 0 ){ five_power_i *= 5; } term = ( product * factorial ) % five_power_E_minus_vN_half; term = ( term * ( uN_minus_power / five_power_i ) ) % five_power_E_minus_vN_half; r = ( r + term ) % five_power_E_minus_vN_half; } kN = ( ( 4 - kN ) % 4 ) / 2; REPEAT( kN ){ r = ( r * zeta ) % five_power_E_minus_vN_half; } REPEAT( vN ){ r *= 5; } r %= five_power_E_minus_vN_half; if( r < bound ){ RETURN( r ); } ll five_power_E = five_power_E_minus_vN_half; REPEAT( vN ){ five_power_E *= 5; } r = five_power_E - r; if( r < bound ){ RETURN( r ); } RETURN( "NaN" ); }