Arul has a binary array$^{\text{∗}}$ $a$ of length $n$.

He will take all subsequences$^{\text{†}}$ of length $k$ ($k$ is odd) of this array and find their median.$^{\text{‡}}$

What is the sum of all these values?

As this sum can be very large, output it modulo $10^9 + 7$. In other words, print the remainder of this sum when divided by $10^9 + 7$.

Input

The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The first line of each test case contains two integers $n$ and $k$ ($1 \leq k \leq n \leq 2 \cdot 10^5$, $k$ is odd) — the length of the array and the length of the subsequence, respectively.

The second line of each test case contains $n$ integers $a_i$ ($0 \leq a_i \leq 1$) — the elements of the array.

It is guaranteed that sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, print the sum modulo $10^9 + 7$.

见题面 Input 部分

见题面 Output 部分

In the first test case, there are four subsequences of $[1,0,0,1]$ with length $k=3$:

• $[1,0,0]$: median $= 0$.
• $[1,0,1]$: median $= 1$.
• $[1,0,1]$: median $= 1$.
• $[0,0,1]$: median $= 0$.

In the second test case, all subsequences of length $1$ have median $1$, so the answer is $5$.