static int waysutil ( int index , int sum , int count , Vector < Integer > arr , int K ) {
  if ( index < 0 ) {
    return 0 ;
  }
  if ( index == 0 ) {
    if ( count == 0 ) {
      return 0 ;
    }
    int remainder = sum % count ;
    if ( remainder != 0 ) {
      return 0 ;
    }
    int average = sum / count ;
    if ( average == K ) {
      return 1 ;
    }
  }
  if ( dp [ index ] [ sum ] [ count ] != - 1 ) {
    return dp [ index ] [ sum ] [ count ] ;
  }
  int dontpick = waysutil ( index - 1 , sum , count , arr , K ) ;
  int pick = waysutil ( index - 1 , sum + arr . get ( index ) , count + 1 , arr , K ) ;
  int total = pick + dontpick ;
  dp [ index ] [ sum ] [ count ] = total ;
  return total ;
}

static int waysutil ( int index , int sum , int count , Vector < Integer > arr , int K ) { if ( index < 0 ) { return 0 ; } if ( index == 0 ) { if ( count == 0 ) { return 0 ; } int remainder = sum % count ; if ( remainder != 0 ) { return 0 ; } int average = sum / count ; if ( average == K ) { return 1 ; } } if ( dp [ index ] [ sum ] [ count ] != - 1 ) { return dp [ index ] [ sum ] [ count ] ; } int dontpick = waysutil ( index - 1 , sum , count , arr , K ) ; int pick = waysutil ( index - 1 , sum + arr . get ( index ) , count + 1 , arr , K ) ; int total = pick + dontpick ; dp [ index ] [ sum ] [ count ] = total ; return total ; }
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