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.IOException;
import java.io.InputStream;
import java.util.Scanner;
import java.util.StringTokenizer;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
 
public class Main {
    static int maxn = (int)(1e5 + 5);
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(System.out);
//        Scanner in = new Scanner(System.in);
        int T = in.nextInt();
        for(int cs = 1; cs <= T; ++cs) {
        	int n = in.nextInt();
        	int x = in.nextInt();
        	String s = in.next();
        	int c1 = 0, a1 = 0;
        	if(x == 0) {
        		++a1;
        	}
        	for(int i = 0; i < n; ++i) {
        		int id = s.charAt(i) - '0';
        		if(id == 0) {
        			++c1;
        		} else {
        			--c1;
        		}
        		if(c1 == x) {
        			++a1;
        		}
        	}
        	if(c1 == 0) {
        		if(a1 == 0) {
        			out.println(0);
        		} else {        			
        			out.println(-1);
        		}
        		continue;
        	}
        	int c2 = 0, a2 = 0;
        	if(x == 0) {
        		++a2;
        	}
        	for(int i = 0; i < n; ++i) {
        		int id = s.charAt(i) - '0';
        		if(id == 0) {
        			++c2;
        		} else {
        			--c2;
        		}
        		if(c1 > 0 && c2 <= x && (x - c2)%c1 == 0) {
        			++a2;
        		}
        		if(c1 < 0 && c2 >= x && (c2 - x)%(-c1) == 0) {
        			++a2;
        		}
        	}
        	out.println(a2);
        }
        out.flush();
//        in.close();
    }
    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());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}

/*


0 1 2 3 4 5 6 7 8 9
6 2 5 5 4 5 6 3 7 6

*/