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 javax.swing.plaf.synth.SynthTextAreaUI;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 *
 */

public class TaskB {

    public static void main(String[] arg) {
        final FastScanner in = new FastScanner(System.in);
        final PrintWriter out = new PrintWriter(System.out);
        final int T = in.nextInt();
        for(int t=0;t<T;t++){
            final int n =  in.nextInt();
            final int x =  in.nextInt();
            final String str = in.next();
            Solution sol = new Solution();
            out.printf("%d%n",sol.solution(n, x, str.toCharArray()));
        }
        out.close();
        in.close();
    }

    private static class Solution{


        public int solution(final int n,
                            int x,
                            char [] s){
            final int [] a = new int[n+1];
            int cnt0=0;
            int cnt1=0;
            a[0]=cnt0-cnt1;
            for(int i=0;i<s.length;i++){
                if('0'==s[i]){
                    cnt0++;
                }
                if('1'==s[i]){
                    cnt1++;
                }
                a[i+1]=cnt0-cnt1;
            }

            int count = 0;
            if(a[n]==0){
                for(int i=0;i<=n;i++){
                    if(a[i]==x){
                        count++;
                    }
                }
                if(count>0){
                    count =-1;
                }
                return count;
            }

            if(a[0]==x){
                count++;
            }

            for(int i=1;i<=n;i++){
                if((x-a[i])%a[n]==0){
                    int cnt = (x-a[i])/a[n];
                    if(cnt>=0)
                    count++;
                }
            }


            return count;

        }

        public void brutForce(int x, int t, final String s) {
            final String t0 = s+s+s+s+s+s+s;
            int cnt0=0;
            int cnt1=0;
            for(int i=0;i<t0.length();i++){
                if(t0.charAt(i)=='1'){
                    cnt1++;
                }
                if(t0.charAt(i)=='0'){
                    cnt0++;
                }
                if(cnt0-cnt1==x){
                    System.out.printf("%d %s%n",i+1,t0.substring(0,i));
                }
            }
        }
    }


    private static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readIntArr(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = Integer.parseInt(next());
            }
            return result;
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        long nextLong() {
            return Long.parseLong(next());
        }

    }
}