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.util.*;
import java.io.*;
import static java.lang.Math.*;
public class Scanner_ {
    //global methods
    static class MyReader {
        BufferedReader br;
        StringTokenizer st;

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

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

        int ni() {
            return Integer.parseInt(ne());
        }

        long nl() {
            return Long.parseLong(ne());
        }

        double nd() {
            return Double.parseDouble(ne());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    public static void main(String[] args) {
        new Thread(null, null, "Rahsut", 1 << 25) {
            public void run() {
                try {
                    Freak();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }
    static long modPow(long x, long p, long m) {
        if (p == 0)
            return 1;
        if (p % 2 == 0)
            return modPow((x * x) % m, p >> 1, m) % m;
        return x * (modPow(x, p - 1, m) % m) % m;
    }
    static long mul(long a, long b, long m) {
        a %= m;
        b %= m;
        return (a * b) % m;
    }
    static long gcd(long a,long b) {
        if(b%a==0)
            return a;
        return gcd(b%a,a);
    }
    static long lcm(long a, long b) {
        a/=gcd(a,b);
        return a*b;
    }
    public static class Pair implements Comparable<Pair> {
        long x, y;
        Pair(long x, long y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(Pair o) {
            if (x != o.x)
                return (int)x - (int)o.x;
            return (int)y - (int)o.y;
        }

        public String toString() {
            return x + " " + y;
        }
    }

    //global variables
    static MyReader sc = new MyReader();
    static StringBuilder sb = new StringBuilder();
    static PrintWriter pw = new PrintWriter(System.out, true);
    static int dir1[][]= {{1,0},{-1,0},{0,1},{0,-1}},n,q,t;
    static int dir2[][] ={{1,-1},{-1,1},{1,1},{-1,-1}};
    static long dp[][], mod = (long)1e9 + 7;
    static void Freak() throws IOException {
        int t =sc.ni();
        while(t-->0) {
            int n= sc.ni(), x = sc.ni(),ans = 0;
            char arr[]= sc.ne().toCharArray();
            int bal[]= new int[n];
            bal[0]=(arr[0]=='0')?1:-1;
            for(int i =1;i<n;i++) {
                bal[i]=bal[i-1] + ((arr[i]=='0')?1:-1);
            }
            if(x==0)
                ans++;
            if(bal[n-1]!=0) {
                for(int i : bal) {
                    if((x-i) % bal[n-1]  == 0 && (x-i)/bal[n-1] >= 0) ans++;
                }
            }else {
                int cnt = 0;
                for(int i : bal)
                    if(i==x) cnt++;
                if(cnt>0) {
                    ans = -1;
                }
            }
            sb.append(ans+"\n");
        }
        pw.println(sb);
        pw.flush();
        pw.close();
    }
}