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.IOException;
import java.io.InputStreamReader;

public class Task1 {

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(reader.readLine());
        String[] str;
        for (int i = 0; i < t; ++i) {
            str = reader.readLine().split(" ");
            int n = Integer.parseInt(str[0]);
            int[] pref = new int[n];
            int x = Integer.parseInt(str[1]);
            int max = Integer.MIN_VALUE;
            int min = Integer.MAX_VALUE;
            String s = reader.readLine();
            int cur = 0;
            int ans = 0;
            for (int j = 0; j < n; ++j) {
                if (s.charAt(j) == '0') {
                    cur++;
                } else {
                    cur--;
                }
                pref[j] = cur;
                max = Math.max(max, cur);
                min = Math.min(min, cur);
            }
            if (cur == 0 && (max >= x && min <= x)) {
                System.out.println(-1);
                continue;
            }
            if (x == 0) {
                ans++;
            }
            if (cur < 0 && max < x) {
                System.out.println(ans);
                continue;
            }
            if (cur == 0) {
                System.out.println(ans);
                continue;
            }
            if (cur > 0) {
                for (int j = 0; j < n; ++j) {
                    if ((x >= pref[j]) && (x - pref[j]) % cur == 0) {
                        ans++;
                    }
                }
            } else {
                for (int j = 0; j < n; ++j) {
                    if ((pref[j] >= x) && (pref[j] - x) % (-cur) == 0) {
                        ans++;
                    }
                }
            }
            System.out.println(ans);
        }
    }
}