Sonya and Informatics

给一个长度为 $n$ $(n\leq 100)$ 的 $0/1$ 串，进行 $k$ $(k \leq 10^9)$ 次操作，每次操作选择两个位置 $i,j$ $(1 \leq i < j \leq n)$，交换 $i,j$ 上的数，求 $k$ 次操作后，该 $0/1$ 串变成非降序列的概率，答案对 $10^9+7$ 取模。

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.

3 2
0 1 0

333333336

5 1
1 1 1 0 0

0

6 4
1 0 0 1 1 0

968493834

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 $ .