public static void main ( String [ ] args ) {
  Scanner in = new Scanner ( System . in ) ;
  int T = in . nextInt ( ) ;
  for ( int t = 0 ;
  t < T ;
  t ++ ) {
    int A = in . nextInt ( ) ;
    int B = in . nextInt ( ) ;
    String S = in . next ( ) ;
    int pos1 = S . indexOf ( '1' ) ;
    int answer = 0 ;
    if ( pos1 != - 1 ) {
      List < Integer > gaps = new ArrayList < > ( ) ;
      while ( true ) {
        int pos0 = S . indexOf ( '0' , pos1 ) ;
        if ( pos0 == - 1 ) break ;
        pos1 = S . indexOf ( '1' , pos0 ) ;
        if ( pos1 == - 1 ) break ;
        gaps . add ( pos1 - pos0 ) ;
      }
      Collections . sort ( gaps ) ;
      answer += A ;
      for ( int gap : gaps ) {
        answer += Math . min ( gap * B , A ) ;
      }
    }
    System . out . println ( answer ) ;
  }
}

public static void main ( String [ ] args ) { Scanner in = new Scanner ( System . in ) ; int T = in . nextInt ( ) ; for ( int t = 0 ; t < T ; t ++ ) { int A = in . nextInt ( ) ; int B = in . nextInt ( ) ; String S = in . next ( ) ; int pos1 = S . indexOf ( '1' ) ; int answer = 0 ; if ( pos1 != - 1 ) { List < Integer > gaps = new ArrayList < > ( ) ; while ( true ) { int pos0 = S . indexOf ( '0' , pos1 ) ; if ( pos0 == - 1 ) break ; pos1 = S . indexOf ( '1' , pos0 ) ; if ( pos1 == - 1 ) break ; gaps . add ( pos1 - pos0 ) ; } Collections . sort ( gaps ) ; answer += A ; for ( int gap : gaps ) { answer += Math . min ( gap * B , A ) ; } } System . out . println ( answer ) ; } }
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