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__":
    t=input()
    t=int(t)
    res=[]
    n=[]
    x=[]
    s=[]
    for i in range(t):
        n1,x1=input().split()
        s1=str(input())
        n1,x1=int(n1),int(x1)
        n.append(n1);x.append(x1);s.append(s1)
    for i in range(t):
        b=[]#b指balance
        b.append(1-2*int(s[i][0]))
        for j in range(1,n[i]):
            b.append(b[j-1]+1-2*int(s[i][j]))
        inc=int(b[-1])
        if inc==0:
            if b.count(x[i]):
                res.append(-1)
            else:
                res.append(0)
            continue
        if inc>0:
            cnt=0
            for j in range(n[i]):
                if (x[i]-b[j])%inc==0  and x[i]-b[j]>=0:
                    cnt+=1
            res.append(cnt)
            continue
        if inc<0:
            cnt=0
            for j in range(n[i]):
                if (x[i]-b[j])%inc==0  and x[i]-b[j]<=0:
                    cnt+=1
            res.append(cnt)
            continue
    for i in range(t):
        if res[i]!=-1:
            res[i]+=int(1-bool(x[i]))
    for i in range(t):
        print(res[i])