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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;
 
public class CodingLegacy {
 
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Palindrome solver = new Palindrome();
 
        int t = in.nextInt();
 
        for(int i=0;i<t;i++) {
            solver.solve(i+1, in, out);
        }
        out.close();
    }
 
    static class Palindrome {
        static long mod = 1000000007;
        static long max = (long) 1e18;
 
        void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int x = in.nextInt();
            char[] s = in.next().toCharArray();
 
            int c= 0;
            for(int i = 0;i<n;i++){
                if(s[i]=='0'){
                    c++;
                } else {
                    c--;
                }
            }
            int p = 0;
            int ans = 0;
 
            for(int i = 0;i<n;i++) {
 
                if(c== 0) {
                    if (x == p){
                        out.println("-1");
                        return;
                    }
                }else if ((x-p)%c == 0) {
 
                    if((x-p)/c >= 0){
                        ans++;
                    }
                }
 
                if(s[i] == '0'){
                    p++;
                } else {
                    p--;
                }
            }
            out.println(ans);
        }
 
        static class Pair {
            int a;
            int b;
 
            Pair(int c,int d) {
                a = c;
                b = d;
            }
        }
    }
 
    static class Maths{
        static long gcd(long a, long b) {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }
 
        public  static long lcm(long a, long b)
        {
            return (a*b)/gcd(a, b);
        }
 
        public static long factorial(int n){
            long fact = 1;
            for(int i=1;i<=n;i++){
                fact *= i;
            }
            return fact;
        }
    }
 
    static class Characters{
        public static boolean isVovel(char a){
            return a == 'a' || a == 'e' || a == 'i' || a == 'o' || a == 'u';
        }
    }
 
    static class Binary {
        public static long numberOfBits(long n){
            long count=0;
            while(n>0){
                count++;
                n >>=1;
            }
            return count;
        }
 
        public static long numberOfSetBits(long n){
            long count = 0;
            int p = 1;
            while (n>0){
                if((n&p) == 1){
                    count++;
                }
                n >>= 1;
            }
            return count;
        }
    }
 
    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;
 
        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        int nextInt(){
            return Integer.parseInt(next());
        }
 
        public Long nextLong(){
            return Long.parseLong(next());
        }
    }
}