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.*;
import static java.lang.Integer.*;
//import static java.lang.Long.*;

public class SF {

	public static void main(String[] args) throws IOException{
		BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out=new PrintWriter(System.out);
		int t=parseInt(in.readLine());
		while(t-->0) {
			String ss[]=in.readLine().split(" ");
			int n=parseInt(ss[0]);
			int x=parseInt(ss[1]);
			String s=in.readLine();
			int arr[]=new int[n+1];
			int ans=0;
			for(int i=0;i<n;i++) {
				int ch=s.charAt(i);
				if(ch=='0')
					arr[i+1]=1;
				else
					arr[i+1]=-1;
			}
			for(int i=1;i<=n;i++)
				arr[i]=arr[i-1]+arr[i];
//			out.println("x= "+x);
//			out.println(Arrays.toString(arr));
			if(x==0)
				ans++;
			if(arr[n]==0) {
				if(x==0)
					ans=-1;
				else {
					for(int i=1;i<=n;i++)
						if(arr[i]==x) {
							ans=-1;
							break;
						}
				}
			}
			else {
				for(int i=1;i<=n;i++) {
					if((x-arr[i])%arr[n]==0 && (x-arr[i])/arr[n]>=0)
						ans++;
				}
			}
			out.println(ans);
			out.flush();
		}
	}

}