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;
import java.util.StringTokenizer;

public class Main {

	static int n,x, arr[];
	static char[] s;

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer tk;
		int casos = Integer.parseInt(bf.readLine());
		int result,temp;
		for (int i = 0; i < casos; i++) {
			result = 0;
			tk = new StringTokenizer(bf.readLine());
			n = Integer.parseInt(tk.nextToken());
			x = Integer.parseInt(tk.nextToken());
			arr = new int[n];
			s = bf.readLine().toCharArray();
			arr[0] = (s[0]=='0'?1:-1);
			for (int j = 1; j < n; j++) {
				arr[j] = arr[j-1];
				if (s[j] == '0') arr[j] ++;
				else arr[j] --;
			}
			temp = arr[n-1];
			if (x == 0) result++;
			if (temp != 0) {
				for (int j = 0; j < n ; j++) {
					if (Math.abs(x - arr[j]) <= Math.abs(x - (arr[j] + temp)) && (x-arr[j]) != 0) continue;
					if ( (x - arr[j]) % temp == 0) {
						result ++;
					}
				}
			} else {
				for (int j = 0; j < n && result != -1; j++) {
					if (x == arr[j])
						result = -1;
				}
			}
			System.out.println(result);
		}

	}
}