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:
//Necessary imports for I/O
import java.io.*;
import java.util.StringTokenizer;
import java.util.HashMap;


public class BInfinitePrefixes {


    public static void main(String[] args) throws IOException {
        
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        StringTokenizer tokenizer;

        tokenizer = new StringTokenizer(reader.readLine());
        int numTests = Integer.parseInt(tokenizer.nextToken());

        for(int i = 0; i<numTests; i++){
            tokenizer = new StringTokenizer(reader.readLine());
            
            int len = Integer.parseInt(tokenizer.nextToken());
            int target = Integer.parseInt(tokenizer.nextToken());
            
            String s = reader.readLine();

            HashMap<Integer, Integer> prefixFreq = new HashMap<>();
            int prefixSum = 0; 
            boolean found = false; 
            for(char c : s.toCharArray()){
                if(c == '1'){
                    prefixSum--; 
                } else {
                    prefixSum++; 
                }
                if(prefixFreq.containsKey(prefixSum)){
                    int count = prefixFreq.get(prefixSum); 
                    count++; 
                    prefixFreq.put(prefixSum, count);
                } else {
                    prefixFreq.put(prefixSum, 1);
                }
            }
            if(prefixSum == 0 && prefixFreq.containsKey(target)){
                writer.write("-1");
                writer.newLine();
                writer.flush(); 
                continue; 
            } else if(prefixSum == 0 && !prefixFreq.containsKey(target)){
                writer.write("0");
                writer.newLine();
                writer.flush(); 
                continue; 
            }
            int count = 0; 
            if(target == 0){
                count++; 
            }
            for(int prefix : prefixFreq.keySet()){
                int numerator = target-prefix;
                if(numerator%prefixSum == 0 && numerator/prefixSum >= 0){
                    count += prefixFreq.get(prefix); 
                }
            }
            writer.write(Integer.toString(count));
            writer.newLine();
            writer.flush(); 
        }

    }
}