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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int T = in.nextInt();
        while (T-- > 0) {
            int n = in.nextInt();
            int x = in.nextInt();
            String s = in.next();
            int cnt = 0;
            for (int i = 0; i < n; ++i) {
                if (s.charAt(i) == '1') {
                    cnt--;
                } else {
                    cnt++;
                }
            }
            if (cnt == 0) {
                if (x == 0) {
                    out.println(-1);
                    continue;
                }
                int balance = 0;
                int f = 0;
                for (int i = 0; i < n; ++i) {
                    if (s.charAt(i) == '1') {
                        balance--;
                    } else {
                        balance++;
                    }
                    if (x == balance) {
                        f++;
                    }
                }
                if (f > 0) {
                    out.println(-1);
                } else {
                    out.println(0);
                }
            } else {
                int balance = 0;
                int f = 0;
                if (x == 0) f++;
                for (int i = 0; i < n; ++i) {
                    if (s.charAt(i) == '1') {
                        balance--;
                    } else {
                        balance++;
                    }
                    if ((x - balance) % cnt == 0 && ((x - balance) / cnt) >= 0) {
                        f++;
                    }
                }
                out.println(f);
            }
        }
        out.close();
    }
}