A12492. Sonya and Informatics

A girl named Sonya is studying in the scientific lyceum of the Kingdom of Kremland. The teacher of computer science (Sonya's favorite subject!) invented a task for her.

Given an array $a$ of length $n$ , consisting only of the numbers $0$ and $1$ , and the number $k$ . Exactly $k$ times the following happens:

- Two numbers $i$ and $j$ are chosen equiprobable such that ( $1 \leq i < j \leq n$ ).
- The numbers in the $i$ and $j$ positions are swapped.

Sonya's task is to find the probability that after all the operations are completed, the $a$ array will be sorted in non-decreasing order. She turned to you for help. Help Sonya solve this problem.

It can be shown that the desired probability is either $0$ or it can be represented as $\dfrac{P}{Q}$ , where $P$ and $Q$ are coprime integers and $Q \not\equiv 0~\pmod {10^9+7}$ .

The first line contains two integers $n$ and $k$ ( $2 \leq n \leq 100, 1 \leq k \leq 10^9$ ) — the length of the array $a$ and the number of operations.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i \le 1$ ) — the description of the array $a$ .

If the desired probability is $0$ , print $0$ , otherwise print the value $P \cdot Q^{-1}$ $\pmod {10^9+7}$ , where $P$ and $Q$ are defined above.

In the first example, all possible variants of the final array $a$ , after applying exactly two operations: $(0, 1, 0)$ , $(0, 0, 1)$ , $(1, 0, 0)$ , $(1, 0, 0)$ , $(0, 1, 0)$ , $(0, 0, 1)$ , $(0, 0, 1)$ , $(1, 0, 0)$ , $(0, 1, 0)$ . Therefore, the answer is $\dfrac{3}{9}=\dfrac{1}{3}$ .

In the second example, the array will not be sorted in non-decreasing order after one operation, therefore the answer is $0$ .