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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;


public class Equal {
    static class pair {
        int v;
        long w;

        public pair(int v, long w) {
            this.v = v;
            this.w = w;
        }


    }

    static class tri implements Comparable<tri> {
        int v, i, j;

        public tri(int v, int i, int j) {
            this.v = v;
            this.i = i;
            this.j = j;
        }

        @Override
        public int compareTo(tri o) {

            return v - o.v;
        }
    }

    static class Node {
        int i;
        long cost;
        int[] child;

        public Node(int ii, long c) {
            i = ii;
            cost = c;
            child = new int[66];
        }
    }

    static ArrayList<pair>[] tree;
    static Node[] nodes;
    static boolean vis[];
    static long sum = 0;

    static void dfs(int u, int p) {
        for (int i = 0; i < tree[u].size(); i++) {
            pair v = tree[u].get(i);
            if (v.v == p)
                continue;

            dfs(v.v, u);
            nodes[u].child[0]++;
            long c = v.w;

            for (int j = 1; j < 66 && c > 0; j++) {
                if (c % 2 == 1)
                    nodes[u].child[j]++;
                c /= 2;
            }
            for (int j = 0; j < 66; j++) {
                nodes[u].child[j] += nodes[v.v].child[j];
            }
            c = v.w;
            for (int j = 1; j < 66; j++) {
                if (c % 2 == 0) {
                    sum += pow(2, j - 1) * nodes[v.v].child[j];
                } else {
                    sum += pow(2, j - 1) * (nodes[v.v].child[0] - nodes[v.v].child[j]);
                }
                c /= 2;
            }
        }
    }

    static long pow(long i, long e) {
        long res = 1;
        while (e-- > 0) {
            res *= i;
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        //BufferedReader br = new BufferedReader(new FileReader("name.in"));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        PrintWriter out = new PrintWriter(System.out);
        int T = Integer.parseInt(br.readLine());
        while (T-- > 0) {
            st = new StringTokenizer(br.readLine());
            int n = Integer.parseInt(st.nextToken());
            int x = Integer.parseInt(st.nextToken());
            String s = br.readLine();
            HashMap<Integer,Integer>b=new HashMap<>();
            int z=0;
            int o=0;
            b.put(0,1);
            int last=0;
            for (int i = 0; i <n ; i++) {
               if(s.charAt(i)=='1')
                   o++;
               else z++;
               if(b.containsKey(z-o))
                   b.replace(z-o,b.get(z-o)+1);
               else b.put(z-o,1);
               if(i==n-1)
                   last=z-o;
            }
            long sum=0;

            if(last==0&&b.containsKey(x))
                sum=-1;
            else {
                if(last==0)
                    sum=0;
                else {
                    for (Map.Entry e : b.entrySet()) {
                        if ((x - (int) e.getKey()) % last == 0 &&(x - (int) e.getKey())/last>=0) {

                            sum += (int) e.getValue();
                            if ((int) e.getKey() == last)
                                sum--;
                        }
                    }
                }

            }
            out.println(sum);


        }
        out.flush();
        out.close();

    }


}