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:
def main():
    T = int(input())
    for i in range (T):
        arr = list(map(int, input().split()))
        N = arr[0]
        X = arr[1]
        str = input()
        summer = 0
        for i in str:
            if i == '0':
                summer += 1
            else:
                summer -= 1
        
        summer2 = 0
        result = 0
        for i in str:
            if i == '0':
                summer2 += 1
            else:
                summer2 -= 1
            if X == summer2 and summer == 0:
                result = -1
                break
        if result == -1:
            print (-1)
            continue
        if summer == 0 and X == 0:
            print(1)
            continue
        if summer == 0:
            print(0)
            continue
        summer2 = 0
        for i in str:
            if i == '0':
                summer2 += 1
            else:
                summer2 -= 1
            if summer2 == X:
                result += 1
                continue
            if summer2 > X and summer > 0:
                continue
            if summer2 < X and summer < 0:
                continue
            if (X - summer2) % summer == 0 and (X - summer2) * summer > 0:
                result += 1
        if X == 0:
            result += 1
        print (result)
            
main()