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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.util.regex.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    
	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc= new Scanner(System.in);
	    int t=sc.nextInt();
	    while(t>0){
	        int n= sc.nextInt();
	        int x= sc.nextInt();
	        //System.out.println(n+"nnnn");
	        int arr[]= new int[n];
	        int zero=0,one=0,count=0;
	        HashSet<Integer> set= new HashSet<>();
	        String s= sc.next();
	        for(int i=0;i<n;i++){
	            int a= Character.getNumericValue(s.charAt(i));
	            if(a==1){
	                one++;
	            }
	            else{
	                zero++;
	            }
	            arr[i]=zero-one;
	            //System.out.println(arr[i]);
	            set.add(arr[i]);
	        }
	        
	        if(arr[n-1]==0){
	            if(set.contains(x)){
	                System.out.println("-1");
	            }
	            else{
	                System.out.println("0");
	            }
	        }
	        
	        else{
	            for(int i=0;i<n;i++){
	                if((x-arr[i])%arr[n-1]==0&&(x-arr[i])/arr[n-1]>=0){
	                    count++;
	                }
	            }
	            if(x==0){
	                count++;
	            }
	            System.out.println(count);
	        }
	        
	        t--;
	    }
	   
	    }
	    	// your code goes here
	}