K Flip CodeChef Solution

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K Flip CodeChef Solution

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Problem

Chef is given a binary string $S$ of length $N$ .

In one operation, Chef has to choose exactly $K$ indices and flip their values.

Chef can perform the above operation any number of times. Find the number of distinct binary strings Chef can obtain.

Since the answer might be large, output it module $10^9 + 7$ .

Input Format

The first line of input will contain a single integer $T$ , denoting the number of test cases.
Each test case consists of multiple lines of input.
- The first line of each test case contains two space-separated integers $N$ and $K$ , as mentioned in statement.
- The next line contains the binary string $S$ .

Output Format

For each test case, output the number of distinct binary strings Chef can obtain, modulo $10^9 + 7$ .

Constraints

$\leq T \leq 10^4$
$\leq N \leq 10^5$
$\leq K \leq N$
Sum of $N$ over all test cases do not exceed $\cdot 10^5$ .

Sample 1:

Input

Output

16
2

Explanation:

Test case $1$ : We can flip $1$ index in an operation. Thus, we can generate all possible binary strings of length $4$ . The total number of distinct strings that can be generated are $2^4 = 16$ .

Test case $2$ : We have to flip $2$ indices at once. Thus, we can convert $00$ to $11$ . The only possible strings that can be generated are $00$ and $11$ . Thus, the answer is $2$ .

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