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

public class Main {

    private static FastScanner in = new FastScanner();
    private static FastOutputJ out = new FastOutputJ();


    public void run() {
        int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            int len = in.nextInt();
            int want = in.nextInt();
            char[] s = in.next().toCharArray();
            int[] diff = new int[s.length];

            boolean anyEqual = false;
            long ans = 0;

            for (int j = 0; j < s.length; j++) {
                int prev = j == 0 ? 0 : diff[j - 1];
                diff[j] = prev + (s[j] == '0' ? 1 : -1);

                if (diff[j] == want) {
                    anyEqual = true;
//                    ans++;
                }
            }

            int totalDiff = diff[diff.length - 1];

            if (want == 0) {
                ans++;
            }

            if (totalDiff == 0) {
                if (anyEqual) {
                    out.println("-1");
                } else {
                    out.println(ans);
                }
                continue;
            }
            for (int j = 0; j < diff.length; j++) {
                int a = (want - diff[j]);
                int b = totalDiff;
                if (a < 0 && b >= 0 || a > 0 && b <= 0) {
                    continue;
                }
                if (b < 0 && a < 0) {
                    a = -a;
                    b = -b;
                }
                if (a % b == 0) {
                    ans++;
                }
            }
            out.println(ans);
        }
    }

    public static void main(String[] args) {
        new Main().run();
        out.flush();
        out.close();
    }
}

class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    FastScanner() {
        this(System.in);
    }

    FastScanner(InputStream stream) {
        br = new BufferedReader(new InputStreamReader(stream));
    }

    FastScanner(File file) {
        try {
            br = new BufferedReader(new FileReader(file));
        } catch (FileNotFoundException e) {
            throw new RuntimeException(e);
        }
    }

    String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }

        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    public String nextLine() {
        try {
            return br.readLine();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
}

class FastOutputJ {
    private final BufferedWriter bf;


    public FastOutputJ(OutputStream outputStream) {
        bf = new BufferedWriter(new OutputStreamWriter(outputStream));
    }

    public FastOutputJ() {
        this(System.out);
    }

    private void printOne(Object s) {
        try {
            bf.write(s.toString());
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void println(Object s) {
        printOne(s);
        printOne("\n");
    }

    public void print(Object... os) {
        printd("", os);
    }

    public void printd(String delimiter, Object... os) {
        for (Object o : os) {
            printOne(o);
            printOne(delimiter);
        }
    }

    public void flush() {
        try {
            bf.flush();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void close() {
        try {
            bf.close();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
}