Consider a binary string of length $$$n$$$ and an odd number $$$k$$$. We will call the binary string good if for each substring of length $$$k$$$, the leftmost character of the substring occurs more than the other.

For example, if $$$k = 3$$$, 000101 is a good string, because for all substrings of length 3 (000, 001, 010, and 101) the first character of the substring occurs more than the other character. On the other hand, 1011 is not good, because the property is false for 011.

Given a pattern of length $$$n$$$ consisting of characters 0, 1 and ?, find the number of ways to replace question marks with 0 or 1, such that the resulting binary string is good. Since the answer may be large, find it modulo $$$998\,244\,353$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$3 \le k \le n \le 10^5$$$, $$$k$$$ is odd). The second line contains $$$n$$$ characters 0, 1 or ? — the pattern.

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

Output

For each test case, print the number of ways to replace ? with 0 or 1 such that the resulting string is good, modulo $$$998\,244\,353$$$.

Note

In the first example, three valid ways to make the pattern good are 00000, 00001, and 00101. In the second example, the only invalid way (out of 16 total ways) is 1001001.

Left is Always Right

Examples