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 Main2 {
	static class FastReader{ 
        BufferedReader br; 
        StringTokenizer st; 
        public FastReader(){br = new BufferedReader(new InputStreamReader(System.in));}
        String next(){while (st == null || !st.hasMoreElements()){try{st = new StringTokenizer(br.readLine());} 
        catch (IOException  e){e.printStackTrace();}}return st.nextToken();}
        int nextInt(){ return Integer.parseInt(next());}long nextLong(){return Long.parseLong(next());}double nextDouble(){return Double.parseDouble(next());}
        String nextLine(){String str = ""; try{str = br.readLine(); } catch (IOException e) {e.printStackTrace();} return str; } 
    }
	static int mod = (int)(1e9+7);
	static FastReader sc = new FastReader();
	static PrintWriter out = new PrintWriter(System.out);
	public static void main (String[] args) {
		int t = 1;
    	t = sc.nextInt();
	    z : while(t-->0) {
	    	int n = sc.nextInt();
	    	int x = sc.nextInt();
	    	char s[] = sc.next().toCharArray();
	    	int cnt0 = 0, cnt1 = 0;
	    	for(int i=0;i<n;i++) {
	    		if(s[i] == '0') cnt0++;
	    		else cnt1++;
	    	}
	    	int total = cnt0 - cnt1;
	    	int bal = 0;
	    	boolean is = false;
	    	int ans = 0;
	    	for(int i=0;i<n;i++) {
	    		if(total == 0) {
	    			if(bal == x) is = true;
	    		}
	    		else if(Math.abs(x - bal)%Math.abs(total) == 0) {
	    			if((x-bal)/total>=0) ans++;
	    		}
	    		if(s[i] == '0') bal++;
	    		else bal--;
	    	}
	    	if(is) out.write("-1\n");
	    	else out.write(ans+"\n");
		}
		out.close();
	}
}