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.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
  public static void main(final String[] args) {
    Scanner scanner = new Scanner(System.in);
    int tests = scanner.nextInt();

    for (int i = 0; i < tests; i += 1) {
      int len = scanner.nextInt();
      int wanted = scanner.nextInt();
      scanner.nextLine();
      String conf = scanner.nextLine();

      int res = solve(conf, wanted);
      System.out.println(res);
    }
  }

  private static int solve(final String conf, final int wanted) {
    Map<Integer, Integer> deltaCount = new HashMap<>();
    int delta = 0;

    for (final char ch : conf.toCharArray()) {
      delta += (ch == '0' ? 1 : -1);
      deltaCount.put(delta, 1 + deltaCount.getOrDefault(delta, 0));
    }

    if (delta == 0) {
      return deltaCount.containsKey(wanted) ? -1 : (wanted == 0 ? 1 : 0);
    }

    int total = 0;
    for (final Map.Entry<Integer, Integer> entry : deltaCount.entrySet()) {
      boolean goodSteps = ((wanted - entry.getKey()) % delta == 0);
      boolean goodDirection = ((wanted - entry.getKey()) / delta >= 0);

      if (goodSteps && goodDirection) {
        total += entry.getValue();
      }
    }
    return total + (wanted == 0 ? 1 : 0);
  }
}