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.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class C {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(in.nextInt(), in, out);
        out.close();
    }
    static class TaskA {
        int leaf = 0;
        class Combine{
            int value , delete;
            Combine(int val , int delete){
                this.value = val;
                this.delete = delete;
            }
        }
        class Sort implements Comparator<Combine>{
            public int compare(Combine a , Combine b){
                if(a.value > b.value)
                    return 1;
                else if(a.value == b.value && a.delete>b.delete)
                    return 1;
                return -1;
            }
        }
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            while(testNumber-->0){
                int n = in.nextInt();
                long s = in.nextLong();
                String d = in.next();
                int a[] = new int[n];
                a[0] = d.charAt(0)=='0'?1:-1;
                for(int i=1;i<n;i++){
                    a[i] = a[i-1];
                    char b = d.charAt(i);
                    if(b == '1')
                        a[i]--;
                    else
                        a[i]++;
                }
                // for(int i=0;i<n;i++)
                //     out.print(a[i]);
                // out.println(a);
                if(s==0 && a[n-1]==0){
                    out.println(-1);
                    continue;
                }
                int count = 0;
                for(int i=0;i<n;i++){
                    if(a[n-1]==0 && a[i] == s){
                        count = -1;
                        break;
                    }
                    if(a[n-1]!=0 && Math.ceil((double)(s - a[i])/a[n-1]) == Math.floor((double)(s - a[i])/a[n-1])){
                        long x = (s - a[i])/a[n-1];
                        if(x>=0)
                            count++;
                    }
                }
                if(a[n-1] == 0 && count != 0)
                    out.println(-1);
                else if(s == 0)
                    out.println(count+1);
                else
                    out.println(count);
            }
        }
    }

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

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            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 int nextInt() {
            return Integer.parseInt(next());
        }

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

    }
}