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 ≤ i < j ≤ 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 P/Q, where P and Q are coprime integers and Q not≡ 0~\pmod {10^9+7}.

Input

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

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 1) — the description of the array a.

Output

If the desired probability is 0, print 0, otherwise print the value P ⋅ 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 3/9=1/3.

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

inputFormat

Input

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

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 1) — the description of the array a.

outputFormat

Output

If the desired probability is 0, print 0, otherwise print the value P ⋅ 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 3/9=1/3.

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

样例

3 2
0 1 0

333333336

</p>