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.StringTokenizer;

public class B {

    FastScanner scanner;
    PrintWriter writer;

    void solve() throws IOException {
        scanner = new FastScanner(System.in);
        writer = new PrintWriter(System.out);

        int tests = scanner.nextInt();

        for (int t = 0; t < tests; t++) {
            int n = scanner.nextInt();
            int x = scanner.nextInt();

            int[] bs = new int[n + 1];
            bs[0] = 0;

            String s = scanner.nextLine().trim();
            boolean met = x == 0;

            for (int i = 0; i < n; i++) {
                char c = s.charAt(i);

                int d;

                if (c == '0') {
                    d = 1;
                } else {
                    d = -1;
                }
                bs[i + 1] = bs[i] + d;

                if (bs[i + 1] == x) {
                    met = true;
                }
            }
            int b = bs[n];
            if (b == 0) {
                if (met) {
                    writer.println(-1);
                } else {
                    writer.println(0);
                }
            } else {
                int ans = 0;
                for (int i = 0; i < n; i++) {
                    int diff = x - bs[i];
                    if (diff / b >= 0 && diff % b == 0) {
                        ans++;
                    }
                }
                writer.println(ans);
            }
        }

        writer.close();
    }

    public static void main(String... args) throws IOException {
        new B().solve();
    }

    static class FastScanner {

        BufferedReader br;
        StringTokenizer tokenizer;

        FastScanner(String fileName) throws FileNotFoundException {
            this(new FileInputStream(new File(fileName)));
        }

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

        String nextLine() throws IOException {
            tokenizer = null;
            return br.readLine();
        }

        String next() throws IOException {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = br.readLine();
                if (line == null) {
                    return null;
                }
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }

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

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    }
}