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 bisect

from sys import stdin
input=stdin.readline
for xoxo in range(1):

    #ans=0
    for _ in range (int(input())):
        a=[]
        n,x=map(int, input().split())
        s=input()
        zc=s.count('0')
        oc=s.count('1')
        for i in range(n):
            a.append(int(s[i]))
        #print(a)    
        b=[]
        k=0
        for i in range(n):
            if a[i]==0:
                k+=1
            else:
                k-=1
            b.append(k)
        if zc==oc:
            k=0
            if b.count(x)==0:
                ans=0
            else:
                ans=-1
        else:        
            k=zc-oc
            if k>0:
                for i in range(n):
                    if abs(x-b[i])%k==0 and x>=b[i]:
                        b[i]=x
            else:
                for i in range(n):
                    if abs(b[i]-x)%k==0 and x<=b[i]:
                        b[i]=x
                        
            ans=b.count(x)
       
        if x==0 and ans!=-1:
            print(ans+1)
        else:    
            print(ans)        
    #ans=[]
    #
    #a=list(map(int, input().split()))