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:
import sys,math
for _ in range(int(input())):
    n,x = map(int,input().split())
    a = str(input())
    ans = 0
    z = 0
    o = 0
    if x<0:
        tmp = []
        for i in range(n):
            if a[i]=='0':
                tmp.append('1')
            else:
                tmp.append('0')
        del a
        a = []
        for i in range(n):
            a.append(tmp[i])
        x*=-1
    for i in range(n):
        if a[i]=='0':
            z+=1
        else:
            o+=1
        if z-o==x:
            ans+=1
    d = z - o
    c1 = 0
    c2 = 0
    if d==0 :
        if ans>0:
            print(-1)
        else:
            print(0)
        continue
    if x==0:
        ans+=1
    z = 0
    o = 0
    for i in range(n):
        if a[i]=='0':
            z+=1
        else:
            o+=1
        if d>=0:
            var = x - (z - o)
            if var>0 and var%d==0:
                ans+=1
        else:
            var = x - (z - o)
            var*=-1
            D=d*-1
            if var>0 and var%D==0:
                ans+=1
    print(ans)