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:
t = int(input())
for i in range(t):
    n, x = map(int,input().split())
    s = input()
    j = 0
    mi = 2*n+10
    A = [0] * (4*n+20)
    xx = x

    for k in range(n):
        if s[k] == "1":
            j -= 1
        else:
            j += 1
        A[j+mi] += 1
    ans = 0
    # print("j",j)
    if j != 0:
        if x >= n+2 and j > 0:
            x = n+2 + ((x-n-2)%j)
        elif x <= -n-2 and j < 0:
            x = -n-2 + ((x+n+2)%abs(j)) + j
        s = x+mi

        while 0 <= s < len(A):
            ans += A[s]
            s -= j
            # print("ans",ans,s)
    else:
        if 0 <= x+mi < len(A) and A[x+mi] > 0:
            ans = -1
        else:
            ans = 0
    if ans != -1 and xx == 0:
        ans += 1
    print(ans)