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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    final static long MOD = 1000000007;

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);



        int t = fs.nextInt();

        while(t > 0) {
            t-=1;
            int n = fs.nextInt();
            int x = fs.nextInt();
            int [] a = new int [n];
            String s = fs.next();
            int zero = 0;
            int one = 0;
            for(int i = 0; i < n; i++) {
                if(s.charAt(i) == '0') {
                    zero++;
                } else {
                    one++;
                }
                a[i] = zero - one;
            }


            if(a[n-1] == 0) {
                boolean found = Arrays.stream(a).anyMatch(val -> val == x);
                if(found) out.println("-1");
                else {
                    out.println("0");
                }
            } else {
                int ansc = 0;
                if(x==0)
                    ansc++;
                for(int i = 0; i < n; i++) {
                    double start = a[i];
                    int d = a[n-1];
                    double term = (((x*1.0) - start)/d) + 1*1.0;
                    //out.println(term);
                    if(Math.floor(term) == term && term > 0) {
                        //System.out.println("--"+term+"--"+"--"+a[i]);
                        ansc++;
                    }
                }
                out.println(ansc);
            }
        }
        out.flush();
        out.close();
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            try {
                br = new BufferedReader(new InputStreamReader(System.in));
                //                br = new BufferedReader(new FileReader("file2.txt"));
                st = new StringTokenizer("");
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        public String next() {
            if (st.hasMoreTokens())
                return st.nextToken();
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            String line = "";
            try {
                line = br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return line;
        }

        public char nextChar() {
            return next().charAt(0);
        }

        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        public char[] nextCharArray() {
            return nextLine().toCharArray();
        }
    }

}

class Pair implements Comparable<Pair> {

    int first;
    int second;

    public Pair(int count, int val) {
        this.first = count;
        this.second = val;
    }

    @Override
    public int compareTo(Pair o) {
        if(this.first != o.first)
            return Integer.compare(this.first, o.first);
        else
            return Integer.compare(this.second, o.second);
    }
}