F. Sonya and Informatics
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$Q \not\equiv 0~\pmod {10^9+7}$$$.

Input

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 $$$a$$$.

Output

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.

Examples
Input
3 2
0 1 0
Output
333333336
Input
5 1
1 1 1 0 0
Output
0
Input
6 4
1 0 0 1 1 0
Output
968493834
Note

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 $$$0$$$.