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:
//package main;
import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.*;
public class Submission {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter (System.out);
        //BufferedReader reader = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt")));
        //StringTokenizer st = new StringTokenizer(reader.readLine()," ");
        int t = Integer.parseInt(reader.readLine());
        for (int i=0;i<t;i++) {
        	StringTokenizer st = new StringTokenizer(reader.readLine()," ");
        	int n = Integer.parseInt(st.nextToken());
        	int x = Integer.parseInt(st.nextToken());
        	String s = reader.readLine();
        	int[] vals = new int[2*n+1]; //0 is n
        	int count=0;
        	for (int j=0;j<n;j++) {
        		vals[count+n]++;
        		if (s.charAt(j)=='0') count++;
        		else count--;
        	}
        	int searchval = x+n;
        	int answer=0;
        	if (count!=0) {
        		if (count>0) for (int j=0;j<=2*n;j++) {if (((searchval-j)%count==0)&&j<=searchval) answer+=vals[j];}
        		else for (int j=0;j<=2*n;j++) if (((searchval-j)%(0-count)==0)&&j>=searchval) answer+=vals[j];
        	} else {
        		if (0<=searchval&&searchval<=2*n&&vals[searchval]>0) answer=-1;
        	}
        	out.println(answer);
        }
        reader.close();
        out.close();
    }
}