static int countNum ( int idx , int sum , int tight , Vector < Integer > num , int len , int k ) {
  if ( len == idx ) {
    if ( sum == 0 ) return 1 ;
    else return 0 ;
  }
  if ( dp [ idx ] [ sum ] [ tight ] != - 1 ) return dp [ idx ] [ sum ] [ tight ] ;
  int res = 0 , limit ;
  if ( tight == 0 ) {
    limit = num . get ( idx ) ;
  }
  else {
    limit = 9 ;
  }
  for ( int i = 0 ;
  i <= limit ;
  i ++ ) {
    int new_tight = tight ;
    if ( tight == 0 && i < limit ) new_tight = 1 ;
    res += countNum ( idx + 1 , ( sum + i ) % k , new_tight , num , len , k ) ;
    res %= MOD ;
  }
  if ( res < 0 ) res += MOD ;
  return dp [ idx ] [ sum ] [ tight ] = res ;
}

static int countNum ( int idx , int sum , int tight , Vector < Integer > num , int len , int k ) { if ( len == idx ) { if ( sum == 0 ) return 1 ; else return 0 ; } if ( dp [ idx ] [ sum ] [ tight ] != - 1 ) return dp [ idx ] [ sum ] [ tight ] ; int res = 0 , limit ; if ( tight == 0 ) { limit = num . get ( idx ) ; } else { limit = 9 ; } for ( int i = 0 ; i <= limit ; i ++ ) { int new_tight = tight ; if ( tight == 0 && i < limit ) new_tight = 1 ; res += countNum ( idx + 1 , ( sum + i ) % k , new_tight , num , len , k ) ; res %= MOD ; } if ( res < 0 ) res += MOD ; return dp [ idx ] [ sum ] [ tight ] = res ; }
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