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.*;
import java.io.*;
 
public class Solution{
	long rem = 1000000007L;
	public Solution(){
		Scanner sc = new Scanner(System.in);
		int tests = sc.nextInt();
        
        for(int t=1; t<=tests; t++){
			int n = sc.nextInt();
			int x = sc.nextInt();
			
			String str = sc.next();
			//HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
			int c = 0;
			
			int[] arr = new int[n];
			if(str.charAt(0) == '0'){
				arr[0] = 1;
			}
			else{
				arr[0] = -1;
			}
			//map.put(x-arr[0], 1);
			
			for(int i=1; i<n; i++){
				if(str.charAt(i) == '0'){
					arr[i] = arr[i-1]+1;
				}
				else{
					arr[i] = arr[i-1]-1;
				}
				//map.put(x-arr[i], map.getOrDefault(x-arr[i], 0)+1);
			}
			
			int count = 0;
			int initial = 0;
			if(x == 0){
				count++;
			}
			
			for(int i=0; i<n; i++){
				if(arr[i] == x){
					count++;
				}
			}
			
			if(arr[n-1] == 0){
				if(count == 0){
					System.out.println(count);
				}
				else{
					System.out.println("-1");
				}
				continue;
			}
			
			for(int i=0; i<n; i++){
				int num = x-arr[i];
				if(num == 0){
					continue;
				}
				else{
					if((num < 0 && arr[n-1] < 0) || (num > 0 && arr[n-1] > 0)){
						if(num % arr[n-1] == 0){
							count++;
						}
					}
				}
			}
			
			System.out.println(count);
        }
	}
	
	public static void main(String[] args){
		new Solution();
	}
}