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.lang.reflect.Array;
import java.util.*;

public class B {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

    static int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }

    static boolean isPrime(int n) {
        //check if n is a multiple of 2
        if (n % 2 == 0) return false;
        //if not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
        int t = ri();
//        int t=1;
        while (t-- > 0)
        {
            int n=ri();
            long x=rl();
            char[] arr=rs().toCharArray();
            TreeMap<Integer,Integer> map=new TreeMap<>();
            int[] dp=new int[n];
//            dp[0]=1;
            if(arr[0]=='1')
            {
                if(x>=0) {
                    dp[0] = -1;
                }
                else
                {
                    dp[0]=1;
                }
            }
            else
            {
                if(x>=0) {
                    dp[0] = 1;
                }
                else
                {
                    dp[0]=-1;
                }
            }

            for(int i=1;i<n;i++)
            {
                dp[i]=dp[i-1];
                if(arr[i]=='0')
                {
                    if(x>=0) {
                        dp[i]++;
                    }else
                    {
                        dp[i]--;
                    }
                }
                else
                {
                    if(x>=0) {
                        dp[i]--;
                    }else
                    {
                        dp[i]++;
                    }
                }
            }
            if(dp[n-1]==0)
            {
                x=Math.abs(x);
                int flag=0;
                for(int i:dp)
                {
                    if(i==x)
                    {
                        flag=1;
                        break;
                    }
                }
                if(flag==1)
                {
                    ans.append("-1\n");
                }
                else
                {

                    ans.append("0\n");
                }
                continue;

            }
//            int max=Integer.MIN_VALUE;
//            for(int i:dp)
//            {
//                System.out.print(i+" ");
////                max=Math.max(i,max);
//            }
//            System.out.println();
            x=Math.abs(x);
            int last=dp[n-1];
            long count=0;
            if(x==0)
            {
                count++;
            }
            for(int i:dp)
            {
                long val=  (x-i);

                if(val%last==0)
                {
//                    System.out.println(val);
                    val=val/last;
                    if(val>=0)
                    {
                        count++;
                    }
                }
            }
            ans.append(count).append("\n");

        }
        out.print(ans.toString());
        out.flush();

    }

}