#include using namespace std; using ll = long long; #define TYPE_OF( VAR ) remove_const::type >::type #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define CEXPR( LL , BOUND , VALUE ) constexpr const LL BOUND = VALUE #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 FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR >= FINAL ; VAR -- ) #define QUIT return 0 #define RETURN( ANSWER ) cout << ( ANSWER ) << "\n"; QUIT class NM { public : ll m_N; ll m_M; inline NM( const ll& N = 0 , const ll& M = 0 ) : m_N( N ) , m_M( M ) {}; }; inline bool operator<( const NM& NM0 , const NM& NM1 ) { return NM0.m_N < NM1.m_N; } template INT GCD( const INT& b_0 , const INT& b_1 ) { INT b[2] = { b_0 , b_1 }; int i_0 = ( b_0 >= b_1 ? 0 : 1 ); int i_1 = 1 - i_0; while( b[i_1] != 0 ){ b[i_0] %= b[i_1]; swap( i_0 , i_1 ); } return b[i_0]; } int main() { CEXPR( ll , bound_PQ , 1000000000 ); CIN_ASSERT( P , 1 , bound_PQ ); CIN_ASSERT( Q , 1 , bound_PQ ); CEXPR( ll , rQ , 31622 ); NM answer[rQ]; // N = ab , M = bc , b = gcd( N , M ) // 1/N + 1/M = (a+c) / abc // gcd( a + c , ac ) = 1 , ac | Q ll b , c , N , M; int T = 0; FOREQ( a , 1 , Q ){ if( a * a > Q ){ break; } if( Q % a == 0 ){ c = Q / a; if( GCD( a , c ) == 1 ){ b = ( ( ( ( a + c ) * Q ) / P ) / a ) / c; if( ( a + c ) * Q == a * b * c * P ){ N = a * b; M = b * c; if( N > 0 && M > 0 ){ answer[T] = NM( N , M ); T++; if( N != M ){ answer[T] = NM( M , N ); T++; } } } } } } cout << T << "\n"; sort( answer , answer + T ); FOR( t , 0 , T ){ NM& NMt = answer[t]; cout << NMt.m_N << " " << NMt.m_M << "\n"; } QUIT; }