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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Que {

    void solve() throws IOException {

        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while(t-->0) {
            int n = sc.nextInt();
            int x = sc.nextInt();
            int[] count = new int[n];
            String s = sc.next();
            for(int i = 0; i < n; i++) {
                if(i > 0) count[i] = count[i-1];
                if(s.charAt(i) == '0') count[i] += x < 0 ? -1 : 1;
                else count[i] += x < 0 ? 1 : -1;
            }
            x = Math.abs(x);
            int ans = x == 0 ? 1 : 0;
            if(count[n-1] < 0) {
                for(int i = 0; i < n; i++) {
                    if(count[i] >= x && (count[i] - x) % (-count[n-1]) == 0) ans++;
                }
                System.out.println(ans);
            }
            else if(count[n-1] == 0) {
                for(int i = 0; i < n; i++) if(count[i] == x) ans++;
                System.out.println(ans == 0 ? 0 : -1);
            }
            else {
                for(int i = 0; i < n; i++) {
                    if(count[i] <= x && (x - count[i]) % count[n-1] == 0) ans++;
                }
                System.out.println(ans);
            }
        }
    }

    public static void main(String[] args) throws IOException {
        // TODO Auto-generated method stub
        new Que().solve();
    }

    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;
        }
    }
}