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 {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=input.nextInt();
        while(T-->0)
        {
            int n=input.nextInt();
            int x=input.nextInt();
            String s=input.next();
            int pre[]=new int[n];
            for(int i=0;i<n;i++)
            {
                int a=0;
                if(s.charAt(i)=='1')
                {
                    a=-1;
                }
                else
                {
                    a=1;
                }
                if(i==0)
                {
                    pre[i]=a;
                }
                else
                {
                    pre[i]=pre[i-1]+a;
                }
            }
            /*
            for(int i=0;i<n;i++)
            {
                out.print(pre[i]+" ");
            }
            out.println();

             */
            int a=pre[n-1];
            int count=0;
            if(a==0)
            {
                for(int i=0;i<n;i++)
                {
                    if(pre[i]==x)
                    {
                        count++;
                    }
                }
                if(count>0)
                {
                    out.println(-1);
                }
                else
                {
                    out.println(0);
                }
            }
            else
            {
                for(int i=0;i<n;i++)
                {
                    int b=x-pre[i];
                    if(b%a==0 && b/a>=0)
                    {
                        count++;
                    }
                }
                if(x==0)
                {
                    count++;
                }
                out.println(count);
            }
        }
        out.close();
    }
    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;
        }
    }
}