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.*;

public class Main {

    static HashMap<Integer, Integer> map_add(HashMap<Integer, Integer> map, int x) {
        if (map.containsKey(x)) {
            map.put(x, map.get(x)+1);
        } else {
            map.put(x, 1);
        }
        return map;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for (int i=0;i<t;i++) {
            int n = sc.nextInt();
            int x = sc.nextInt();
            String s = sc.next();
            int[] arr = new int[n];
            for (int j=0;j<n;j++) {
                if (s.charAt(j)=='0') arr[j] = 1;
                else arr[j]=-1; // s.charAt(j)=='1'
            }
            int[] ruiseki = new int[n+1];
            int max = 0;
            int min = 0;
            HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
            for (int j=0;j<n;j++) {
                ruiseki[j+1] = ruiseki[j]+arr[j];
                max = Math.max(max, ruiseki[j+1]);
                min = Math.min(min, ruiseki[j+1]);
                map = map_add(map, ruiseki[j+1]);
            }
            if ((ruiseki[n]<=0 && max<x) || (ruiseki[n]>=0 && min>x)) {
                System.out.println(0);
                continue;
            }
            if (ruiseki[n]==0 && (min<=x && x<=max)) {
                System.out.println(-1);
                continue;
            }
            long ans = 0L;
            if (x==0) ans++;
            for (HashMap.Entry<Integer, Integer> entry : map.entrySet()) {
                int key = entry.getKey();
                int value = entry.getValue();
                if ((long)(x-key)*ruiseki[n]>=0 && (x-key)%ruiseki[n]==0) ans += value;
                // System.out.println(entry.getKey());
                // System.out.println(entry.getValue());
            }
            System.out.println(ans);
        }
    }
}