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 InfinitePrefixes {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            int n = in.nextInt();
            int x = in.nextInt();
            String st = in.next();
            int c0 = 0;
            int c1 = 0;
            for (int j = 0; j < st.length(); j++) {
                if(st.charAt(j) == '0'){
                    c0++;
                }else{
                    c1++;
                }
            }
            int end = c0 - c1;
            c0 = 0;
            c1 = 0;
            long ans = x == 0 ? 1 : 0;
            int done = 0;
            for (int j = 0; j < st.length(); j++) {
                if(st.charAt(j) == '0'){
                    c0++;
                }else{
                    c1++;
                }
                int tmp = c0 - c1;
                if(tmp == x && end == 0){
                    System.out.println("-1");
                    done = 1;
                    break;
                }else if(x == tmp){
                    ans++;
                }else if(end > 0 && tmp < x){
                    int mod1 = (Math.abs(tmp % end));
                    int mod2 = (Math.abs(x % end));
                    if(tmp < 0){
                        mod1 = (end - mod1) % end;
                    }
                    if(x < 0){
                        mod2 = (end - mod2) % end;
                    }
                    if(mod2 == mod1){
                        ans++;
                    }
                }else if(end < 0 && tmp > x){
                    int mod1 = (Math.abs(tmp % end));
                    int mod2 = (Math.abs(x % end));
                    if(tmp < 0){
                        mod1 = (-end - mod1) % -end;
                    }
                    if(x < 0){
                        mod2 = (-end - mod2) % -end;
                    }
                    if(mod2 == mod1){
                        ans++;
                    }
                }
            }
            if(done == 0){
                System.out.println(ans);
            }
        }
    }
}