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 calculate_prefixes(s, x):
    new_s = [-1 if value == 1 else 1 for value in s]

    balance = [0] * len(s)
    current_balance = 0
    for i, val in enumerate(new_s):
        current_balance += val
        balance[i] = current_balance

    sum_balance = balance[-1]

    if sum_balance == 0:
        if x in balance:
            return -1
        else:
            return 0

    res = 0
    for value in balance:
        if (x - value) % sum_balance == 0 and (x - value) // sum_balance >= 0:
            res += 1

    # the case with empty prefix
    if x == 0:
        res += 1
    return res


T = int(input())
results = [0] * T
for i in range(T):
    s_len, x = map(int, input().split())
    s = list(map(int, list(input())))
    results[i] = calculate_prefixes(s, x)

for result in results:
    print(result)