Mike and Harvey are back together! To celebrate this special occasion, they decided to play a unique game. So, this is how it goes :

Mike gives Harvey an \(N \times N \) grid A containing integers and 2 integers K and X. Now, Harvey begins the game by selecting K distinct rows among the N rows. He will then add the integer X to all elements of the selected rows.

Mike will then write N integers on a piece of paper, where the \(i^{th}\) integer denotes the maximum integer present in the \(i^{th}\) column. He then tells Harvey the sum of all integers written on that piece of paper. Let's call this number Mike tells Harvey as Z

This is where your part comes in. Considering that Harvey selects each distinct tuple of K rows with equal probability, you are to find the Expected Value of Z. Can you do this ?

Your answer will be considered correct if the absolute OR relative error between your answer and the jury's answer is \( \le 10^{-9} \) . More formally, let your answer be a and the jury's answer be b. Your solution will be considered correct if \( \frac {|a-b|}{max(1,b)} \le 10^{-9} \)

Input Format :

The first line contains 3 space separated integers \(N, K \) and X respectively.

Each of the next N lines contains N space separated integers, where the \(j^{th}\) integer on the \(i^{th}\) line denotes \(A[i][j]\).

Output Format :

For each test case, print a single real number denoting the answer to the problem.

Constraints :

\( 2 \le N \le 1000 \)

\( 1 \le K \le N \)

\( 0 \le A[i] , X \le 10^6 \)