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 JAVA):

Solution:
// Working program with FastReader 
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.ArrayList;
import java.util.*;
  
public class Main 
{ 
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
  
    public static void main(String[] args) 
    { 
         FastReader sc=new FastReader(); 
         int t=sc.nextInt();
         while(t>0)
         {
             t--;
             int n=sc.nextInt();
             long x=sc.nextLong();
             String s=sc.next();
             StringBuilder sb=new StringBuilder(s);
             int i;
            // int max=0;
             int count=0;
             int min=(n+1);
             int max=-(n+1);
             HashMap<Integer,Integer> hm=new HashMap<Integer,Integer>();
             int ar[]=new int[n+1];
             for(i=0;i<(n);i++)
             {
                 if(sb.charAt(i)=='0')
                 {
                 count++;
                 ar[i+1]=ar[i]+1;}
                 else
                 {
                 count--;
                 ar[i+1]=ar[i]-1;
                 }
             }
             int total=count;
              int answer = 0;
            for (i=0; i<n; i++) 
            {
                if (total == 0) 
                {
                    if (ar[i] == x)
                    {
                        answer = -1;
                    }
                }
                else
                {
                    long diff = x-(long) ar[i];
                    if (diff%total == 0 && diff/total >= 0) 
                    {
                        answer++;
                    }
                }
            }
            System.out.println(answer);
            
             
             
         }
          
    } 
    
}