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:
import java.lang.reflect.Array;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;
import java.util.Stack;

public class CodeChef {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0) {
           int n=sc.nextInt();int m=sc.nextInt();
           String s=sc.next();
           int max=0, sum=0;
           int ans=0;
           for (int i=0;i<n;i++){
               if (s.charAt(i)=='0')
                  ++ max;
               else
                   --max;
           }
           for (int i=0;i<n;i++){
               if (max==0){
                   if (sum==m){
                      ans=-1;
                      break;
                   }
               }
               else {
                   if (Math.abs(m-sum)%Math.abs(max)==0) {
                       if ((m - sum) / max >= 0)
                           ++ans;
                   }
               }
               if(s.charAt(i)=='0') ++sum;
               else --sum;
           }
            System.out.println(ans);

        }
    }
}