#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace placeholders; using LL = long long; using ULL = unsigned long long; using VI = vector< int >; using VVI = vector< vector< int > >; using VLL = vector< long long >; using VVLL = vector< vector< long long > >; using VS = vector< string >; using ISS = istringstream; using OSS = ostringstream; using PII = pair< int, int >; using VPII = vector< pair< int, int > >; template < typename T = int > using LIM = numeric_limits< T >; template < typename T = int > using OSI = ostream_iterator< T >; template < typename T > inline istream& operator>>( istream &s, vector< T > &v ){ for ( T &t : v ) { s >> t; } return s; } template < typename T > inline ostream& operator<<( ostream &s, const vector< T > &v ){ for ( int i = 0; i < int( v.size() ); ++i ){ s << ( " " + !i ) << v[i]; } return s; } void in_impl(){}; template < typename T, typename... TS > void in_impl( T &head, TS &... tail ){ cin >> head; in_impl( tail ... ); } #define IN( T, ... ) T __VA_ARGS__; in_impl( __VA_ARGS__ ); template < typename T, typename V > auto make_vector( const int n, const V &v ) { return vector< T >( n, v ); } template < typename T, typename... TS > auto make_vector( const int n, TS... ts ) { return vector< decltype( make_vector< T >( forward< TS >( ts )...) ) >( n, make_vector< T >( forward< TS >( ts )... ) ); } template < typename T, typename V > auto make_vector0() { return vector< T >(); } template < typename T, typename... TS > auto make_vector0( const int n, TS... ts ) { return vector< decltype( make_vector0< T >( forward< TS >( ts )...) ) >( n, make_vector0< T >( forward< TS >( ts )... ) ); } template < typename T > inline T fromString( const string &s ) { T res; istringstream iss( s ); iss >> res; return res; } template < typename T > inline string toString( const T &a ) { ostringstream oss; oss << a; return oss.str(); } #define NUMBERED( name, number ) NUMBERED2( name, number ) #define NUMBERED2( name, number ) name ## _ ## number #define REP1( n ) REP2( NUMBERED( REP_COUNTER, __LINE__ ), n ) #define REP2( i, n ) REP3( i, 0, n ) #define REP3( i, m, n ) for ( int i = ( int )( m ); i < ( int )( n ); ++i ) #define GET_REP( a, b, c, F, ... ) F #define REP( ... ) GET_REP( __VA_ARGS__, REP3, REP2, REP1 )( __VA_ARGS__ ) #define FOR( e, c ) for ( auto &&e : c ) #define ALL( c ) begin( c ), end( c ) #define AALL( a ) ( remove_all_extents< decltype( a ) >::type * )a, ( remove_all_extents< decltype( a ) >::type * )a + sizeof( a ) / sizeof( remove_all_extents< decltype( a ) >::type ) #define MAP_PRED( c ) transform( begin( c ), end( c ), begin( c ), bind( minus< int >(), _1, 1 ) ); #define SZ( v ) ( (int)( v ).size() ) #define EXISTS( c, e ) ( ( c ).find( e ) != ( c ).end() ) template < typename T > inline bool chmin( T &a, const T &b ){ if ( b < a ) { a = b; return true; } return false; } template < typename T > inline bool chmax( T &a, const T &b ){ if ( a < b ) { a = b; return true; } return false; } #define PB push_back #define EM emplace #define EB emplace_back #define BI back_inserter #define MP make_pair #define fst first #define snd second #define DUMP( x ) cerr << #x << " = " << ( x ) << endl // Λ Λ__ // /(*゚ー゚)/\ // /|  ̄U U ̄|\/ // | |/ #include using namespace atcoder; using MINT = modint998244353; inline istream& operator>>( istream &s, MINT &t ){ int a; s >> a; t = a; return s; }; inline istream& operator>>( istream &s, vector< MINT > &v ){ for ( MINT &a : v ){ s >> a; } return s; } inline ostream& operator<<( ostream &s, const MINT &t ){ s << t.val(); return s; } MINT expected( const MINT &P, const string &S ) { int ma = 0, d = 0; MINT prob = 1; FOR( c, S ) { if ( c == '(' ) { ++d; prob *= P; } else { --d; prob *= P.inv(); } if ( d < 0 ) { return 0; } chmax( ma, d ); } return d ? 0 : ma * prob; } int main() { cin.tie( nullptr ); ios::sync_with_stdio( false ); cout << setprecision( 12 ) << fixed; IN( int, X, K ); assert( K <= 10 ); if ( X == 0 || X == 100 ) { cout << 0 << endl; return 0; } const MINT P = X * MINT( 100 ).inv(); VI is_closing( 2 * K ); fill( begin( is_closing ) + K, end( is_closing ), 1 ); MINT res = 0; do { string s; REP( i, 2 * K ) { s += "()"[ is_closing[i] ]; } res += P.pow( K ) * ( 1 - P ).pow( K ) * expected( P, s ); } while ( next_permutation( ALL( is_closing ) ) ); cout << res << endl; return 0; }