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.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		while(t-->0){
		    int n = s.nextInt();
		    int x = s.nextInt();
		    String a = s.next();
            int count=0;
		    for(int i=0;i<n;i++){
		        if(a.charAt(i)=='0') count++;
		        else count--;
		    }
		    int ans=0;
		    int temp = count;
		    count=0;
		    if(x==0) ans++;
		    if(temp==0){
    		    for(int i=0;i<n;i++){
    		        if(a.charAt(i)=='0') count++;
    		        else count--;
    		        if((x-count)==0){
    		           ans=-1;
    		           break;
    		        }
    		    }
		    }
		    else{
    		    for(int i=0;i<n;i++){
    		        if(a.charAt(i)=='0') count++;
    		        else count--;
    		        if((x-count)%temp==0&&((x-count)/temp)>=0) ans++;
    		    }
		    }
		    System.out.println(ans);
		}
	}
}