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.*;

public class Main {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(in.readLine());
        for (int test = 0; test < t; test++) {
            StringTokenizer st = new StringTokenizer(in.readLine());
            int n = Integer.parseInt(st.nextToken());
            int x = Integer.parseInt(st.nextToken());
            int local = 0;
            String string = in.readLine();
            int[] pSum = new int[n];
            int res = 0;
            for (int i = 0; i < string.length(); i++) {
                if (string.charAt(i) == '0') {
                    local++;
                    pSum[i]++;
                } else {
                    local--;
                    pSum[i]--;
                }
                if (local == x) {
                    res++;
                }
                if (i > 0) {
                    pSum[i] += pSum[i-1];
                }
            }

            if (local == 0) {
                if (res > 0) {
                    System.out.println("-1");
                } else {
                    if (x == 0) {
                        System.out.println("1");
                    } else {
                        System.out.println("0");
                    }
                }
                continue;
            }

            if (x == 0) {
                res++;
            }

            for (int i = 0; i < n; i++) {
                if ((x-pSum[i]) % local == 0) {
                    if (Math.abs(x-pSum[i]) >= Math.abs(pSum[i]+local-x)) {
                        res++;
                    }
                }
            }

            System.out.println(res);
        }
    }

}
/*

 */