#pragma GCC optimize ( "O3" )
#pragma GCC target ( "avx" )
#include <iostream>
#include <string>
#include <stdio.h>
#include <stdint.h>
#include <cassert>
using namespace std;

using ll = long long;

#define TYPE_OF( VAR ) remove_const<remove_reference<decltype( VAR )>::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 REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT , 0 , HOW_MANY_TIMES ) 
#define QUIT return 0 
#define COUT( ANSWER ) cout << ( ANSWER ) << "\n"; 

#define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO )		\
  TYPE_OF( ARGUMENT ) ANSWER{ 1 };					\
  {									\
    TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( MODULO + ( ARGUMENT ) % MODULO ) % MODULO; \
    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;				\
    }									\
  }									\


// POWER_MODを使う
#define FACTORIAL_MOD( ANSWER , ANSWER_INV , MAX_I , LENGTH , MODULO )	\
  static ll ANSWER[LENGTH];						\
  static ll ANSWER_INV[LENGTH];						\
  {									\
    ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1;				\
    ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL;			\
    FOREQ( i , 1 , MAX_I ){						\
      ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= MODULO; \
    }									\
    POWER_MOD( FACTORIAL_MAX_INV , ANSWER[MAX_I] , MODULO - 2 , MODULO ); \
    ANSWER_INV[MAX_I] = FACTORIAL_MAX_INV;				\
    FOREQINV( i , MAX_I - 1 , 0 ){					\
      ANSWER_INV[i] = ( FACTORIAL_MAX_INV *= i + 1 ) %= MODULO;		\
    }									\
  }									\
									\

template <typename INT>
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()
{
  UNTIE;
  CEXPR( int , bound_T , 256 );
  CIN_ASSERT( T , 1 , bound_T );
  CEXPR( ll , bound_HW , 100000 );
  CEXPR( ll , P , 998244353 );
  FACTORIAL_MOD( factorial , factorial_inv , bound_HW , bound_HW + 1 , P );
  ll answer, gcd , sum , r , j , j_rest;
  REPEAT( T ){
    CIN_ASSERT( H , 4 , bound_HW );
    CIN_ASSERT( W , 4 , bound_HW );
    answer = H * W;
    gcd = GCD<ll>( H , W );
    if( gcd > 3 ){
      answer += gcd * 2;
      if( gcd > 4 ){
	if( ( ( H * W ) / gcd ) % 3 == 0 ){
	  answer += gcd * 12;
	}
      }
      if( gcd % 2 == 0 ){
	FOR( i , 0 , 2 ){
	  sum = 0;
	  r = ( gcd + i * 3 ) % 6;
	  j = r == 0 ? 6 : r;
	  // 解説の分類およびパターン５をあまり理解していません。。
	  // とりあえず結果を鵜呑みにしています。すみません。
	  while( ( j_rest = ( gcd / 2 - j * 5 ) / 3 ) >= 0 ){
	    sum += ( factorial[ j - 1 + j_rest ] * ( ( factorial_inv[j] * factorial_inv[j_rest] ) % P ) ) % P;
	    j += 6;
	  }
	  ( ( sum %= P ) *= gcd ) %= P;
	  answer += sum * sum;
	}
	if( gcd % 4 == 0 ){
	  answer += 16;
	}
      }
    }
    COUT( answer % P );
  }
  QUIT;
}