Problem: You are given string s of length n consisting of 0-s and 1-s. You build an infinite string t as a concatenation of an infinite number of strings s, or t = ssss ... For example, if s = 10010, then t = 100101001010010...

Calculate the number of prefixes of t with balance equal to x. The balance of some string q is equal to cnt_{0, q} - cnt_{1, q}, where cnt_{0, q} is the number of occurrences of 0 in q, and cnt_{1, q} is the number of occurrences of 1 in q. The number of such prefixes can be infinite; if it is so, you must say that.

A prefix is a string consisting of several first letters of a given string, without any reorders. An empty prefix is also a valid prefix. For example, the string "abcd" has 5 prefixes: empty string, "a", "ab", "abc" and "abcd".

Input

The first line contains the single integer T (1 ≤ T ≤ 100) — the number of test cases.

Next 2T lines contain descriptions of test cases — two lines per test case. The first line contains two integers n and x (1 ≤ n ≤ 10^5, -10^9 ≤ x ≤ 10^9) — the length of string s and the desired balance, respectively.

The second line contains the binary string s (|s| = n, s_i ∈ \{0, 1\}).

It's guaranteed that the total sum of n doesn't exceed 10^5.

Output

Print T integers — one per test case. For each test case print the number of prefixes or -1 if there is an infinite number of such prefixes.

Example

Input


4
6 10
010010
5 3
10101
1 0
0
2 0
01


Output


3
0
1
-1

Note

In the first test case, there are 3 good prefixes of t: with length 28, 30 and 32.

Solution (in PYTHON3):

Solution:



if __name__ == "__main__":
    for _ in range(int(input())):
        n, x = list(map(int, input().split()))
        s = list(map(int, list(input())))
        for i, num in enumerate(s):
            s[i] = 1 if num == 0 else -1
        firstlevel = []
        csum = 0

        for i in s:
            csum += i
            firstlevel.append(csum)

        secondlevel = []

        for i in s:
            csum += i
            secondlevel.append(csum)
        
        m = len(firstlevel)

        ans = 0 
        if x == 0:
            ans = 1
        # print(firstlevel)
        # print(secondlevel)
        for i in range(m):
            a = firstlevel[i]
            b = secondlevel[i]
            c = b - a

            if a == x:
                if c == 0:
                    ans = -1
                    break
                else:
                    ans += 1
            else:
                difference = x - a
                if difference * c > 0:
                    if difference % c == 0:
                        ans += 1
        
        print(ans)