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.IOException;
import java.io.InputStream;
import java.util.*;
public class CP {
    public static void main(String args[]) throws Exception {
        FastReader in=new FastReader(System.in);
        StringBuilder sb=new StringBuilder();
        int i,j,a,b;
        int t=in.nextInt();
        while(t-->0) {
           int n=in.nextInt();
           int x=in.nextInt();
           String s=in.next();
           int pre[]=new int[n+1];
           HashMap<Integer,Integer> set=new HashMap<>();
           for(i=0;i<n;i++){
               pre[i+1]=pre[i];
               if(s.charAt(i)=='0'){
                   pre[i+1]++;
               }
               else
                   pre[i+1]--;
               if(!set.containsKey(pre[i+1]))
                  set.put(pre[i+1],1);
               else
                   set.put(pre[i+1],set.get(pre[i+1])+1);
           }
            //System.out.println(pre[n]);
           if(set.containsKey(x) && pre[n]==0) {
               sb.append("-1\n");
               continue;
           }
           else if(pre[n]==0 && !set.containsKey(x)){
               sb.append("0\n");
               continue;
           }
           int ans=0;
           if(x==0)
               ans++;
           for(Map.Entry<Integer,Integer> entry:set.entrySet()){
               a=entry.getKey();
               b=entry.getValue();
               //System.out.println(a+" "+b);
               if((x-a)==0){
                   if((x-a)%pre[n]==0 )
                       ans+=b;
               }
               else if((x-a)%pre[n]==0 && (x-a)>0 && pre[n]>0)
                   ans+=b;
               else if((a-x)%(-pre[n])==0 && (x-a)<0 && pre[n]<0)
                   ans+=b;
           }
           sb.append(ans).append("\n");


        }
        System.out.println(sb);



    }
}
class FastReader {

    byte[] buf = new byte[2048];
    int index, total;
    InputStream in;

    FastReader(InputStream is) {
        in = is;
    }

    int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) {
                return -1;
            }
        }
        return buf[index++];
    }

    String next() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }

    String nextLine() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c != 10 && c != 13; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }

    char nextChar() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        return (char) c;
    }

    int nextInt() throws IOException {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }

    long nextLong() throws IOException {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
}