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:
/**
 * Accomplished using the EduTools plugin by JetBrains https://plugins.jetbrains.com/plugin/10081-edutools
 */

import java.util.*;
import java.io.*;

public class Main {
   public static void main(String[] args) throws IOException {
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

      int t = Integer.parseInt(br.readLine());

      while (t-- > 0) {
         String[] line = br.readLine().split(" ");
         int n = Integer.parseInt(line[0]), x = Integer.parseInt(line[1]);
         String s = br.readLine();

         int[] balance = new int[n + 1];
         boolean possible = false;
         for (int i = 0; i < n; ++i) {
            balance[i + 1] = (s.charAt(i) == '1' ? -1 : 1) + balance[i];
            if (!possible && balance[i + 1] == x) {
               possible = true;
            }
         }

         if (balance[n] == 0) {
            bw.write(possible ? "-1\n" : x == 0 ? "1\n" : "0\n");
         } else {
            int sum = 0;

            for (int i = 0; i < n; ++i) {
               if ((x - balance[i]) % balance[n] == 0 && (x == balance[i] || (x < balance[i]) == (balance[n] < 0))) {
                  ++sum;
               }
            }

            bw.write(Integer.toString(sum));
            bw.newLine();
         }
      }

      br.close();
      bw.close();
   }
}