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 Codeforces {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            int n = in.nextInt();
            int x = in.nextInt();

            String s = in.next();

            int total = 0;
            for (int j = 0; j < s.length(); j++) {
                if (s.charAt(j) == '0') {
                    total++;
                } else {
                    total--;
                }
            }

            if (total == 0) {
                boolean inf = false;
                int curBal = 0;
                for (int j = 0; j < s.length(); j++) {
                    int inc = s.charAt(j) == '0' ? 1 : -1;

                    if (curBal == x) {
                        inf = true;
                    }
                    curBal += inc;
                }

                if (inf) {
                    out.println(-1);
                } else {
                    out.println(0);
                }
            } else {
                int curBal = 0;
                int res = 0;
                for (int j = 0; j < s.length(); j++) {
                    int inc = s.charAt(j) == '0' ? 1 : -1;

                    int count = Math.abs((x - curBal) / total);

                    if (x - curBal == total * count) {
                        res++;
                    }
                    curBal += inc;
                }

                out.println(res);
            }
        }

        out.close();
    }

    private static void print2Arr(int[][] arr, PrintWriter out) {
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[0].length; j++) {
                out.print(arr[i][j] + " ");
            }
            out.println();
        }
    }


    private static void printArr(int[] arr, PrintWriter out) {
        for (int i = 0; i < arr.length; i++) {
            out.print(arr[i] + " ");
        }
        out.println();
    }

    public static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            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 String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return null;
        }

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

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

        public int[] nextIntArr(int n) {
            int[] arr = new int[n];
            for (int j = 0; j < arr.length; j++) {
                arr[j] = nextInt();
            }

            return arr;
        }

        public long[] nextLongArr(int n) {
            long[] arr = new long[n];
            for (int j = 0; j < arr.length; j++) {
                arr[j] = nextLong();
            }

            return arr;
        }
    }
}