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 B {
 
    public static void main(String[] args) throws Exception {
        // FileInputStream inputStream = new FileInputStream("input.txt");
        // FileOutputStream outputStream = new FileOutputStream("output.txt");
 
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
         
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
 
        Solver solver = new Solver();     
        int t = in.nextInt();
        // int t = 1;
        for (int i = 0 ; i < t ; i++) {
            solver.solve(1, in, out);
        }
                 
        out.close();
    }
 
    static class Solver {
 
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int x = in.nextInt();
            String s = in.next();
            int[] bal = new int[n + 1];
            if (s.charAt(0) == '0') bal[0] = 1; else bal[0] = -1;
            for (int i = 1 ; i < n ; i++) {
                bal[i] = bal[i - 1];
                if (s.charAt(i) == '0') bal[i] += 1; else bal[i] -= 1;
            }
            bal[n] = bal[n - 1];
            if (s.charAt(0) == '0') bal[n] += 1; else bal[n] -= 1;
            int d = bal[n] - bal[0];
            int res = 0;
            if (d == 0) {
                for (int i = 0 ; i < n ; i++) {
                    if (bal[i] == x) res += 1;
                }
                if (x == 0) res += 1;
                if (res > 0) res = -1;
                out.println(res);
            } else {
                if (x == 0) res = 1;
                for (int i = 0 ; i < n ; i++) {
                    int k = (x - bal[i]) % d;
                    int r = (x - bal[i]) / d;
                    if (k == 0 && r >= 0) res += 1;
                }
                out.println(res);
            }
        }

    }
             
 
    static class InputReader {
 
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
 
        public float nextFloat() {
            return Float.parseFloat(next());
        }
    }
}