public static void main ( String [ ] args ) {
  Scanner sc = new Scanner ( System . in ) ;
  int runs = sc . nextInt ( ) ;
  while ( runs -- > 0 ) {
    int a = sc . nextInt ( ) ;
    int b = sc . nextInt ( ) ;
    char [ ] arr = sc . next ( ) . toCharArray ( ) ;
    int ones = 0 ;
    int zeros = 0 ;
    int out = 0 ;
    for ( int i = 0 ;
    i < arr . length ;
    i ++ ) {
      if ( arr [ i ] == '0' ) zeros ++ ;
      else {
        ones ++ ;
        if ( ones == 1 ) out += a ;
        else out += Math . min ( a , zeros * b ) ;
        zeros = 0 ;
      }
    }
    System . out . println ( out ) ;
  }
}

public static void main ( String [ ] args ) { Scanner sc = new Scanner ( System . in ) ; int runs = sc . nextInt ( ) ; while ( runs -- > 0 ) { int a = sc . nextInt ( ) ; int b = sc . nextInt ( ) ; char [ ] arr = sc . next ( ) . toCharArray ( ) ; int ones = 0 ; int zeros = 0 ; int out = 0 ; for ( int i = 0 ; i < arr . length ; i ++ ) { if ( arr [ i ] == '0' ) zeros ++ ; else { ones ++ ; if ( ones == 1 ) out += a ; else out += Math . min ( a , zeros * b ) ; zeros = 0 ; } } System . out . println ( out ) ; } }
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