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:
nn=int(input())
for i in range(nn):
    n,x=[int(i) for i in input().split(' ')]
    s=input()
    k0=s.count('0')
    k1=s.count('1')
    if (k0-k1==0)and(x==0):
        print(-1)
        continue
    rez=0
    if x==0:
        rez=1
    b=0
    bal=[]
    for j in range(n):
        if s[j]=='1':
            b-=1
        else:
            b+=1
        bal.append(b)
    #print(bal)
    if s[0]=='1':
        b-=1
    else:
        b+=1
    shag=b-bal[0]
    #print(shag)
    if shag!=0:
        for j in range(n):
            if ((x-bal[j])%shag==0)and((bal[j]==x)or(abs(bal[j]+shag-x)<=abs(bal[j]-x))):
                rez+=1
    else:
        for j in range(n):
            if bal[j]==x:
                rez+=1
        if rez>0:
            rez=-1
    print(rez)