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.*;
import java.math.BigInteger;
import java.util.*;
import java.util.Stack;

public class ROUGH{
	public static class FastReader {
		BufferedReader br;
		StringTokenizer root;
		
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (root == null || !root.hasMoreTokens()) {
				try {
					root = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return root.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	static int mod = (int) (1e9+7);
	static long cf = 998244353;
    static final int N = (int) 1e3+10;
    public static List<Integer>[] edges;
    public static int[][] parent;
    public static int col = 20;
    public static int[] Bit;
    public static long[] fact,inv;
    public  static int[] prime; 
	public static Map<Integer, Integer> map; 
	static char ch = 'z';
	static FastReader sc = new FastReader();
	public static void main(String[] args) {
	//	Scanner sc = new Scanner(System.in);
int T = sc.nextInt();
		
		while ((T--) != 0){
			
			int n = sc.nextInt();
			int x = sc.nextInt();
			char[] s = sc.next().toCharArray();
			int total = 0;
			for (char c : s){
				if (c == '0') ++total;
				else --total;
			}
			
			long ans = 0, cur = 0;
			for (char c : s){
				if (total == 0) {
					if(cur == x){
						ans = -1;
						break;
				       }
				   }else if ((x - cur) % total == 0 && (x - cur) / total >= 0)
					++ans;
				    if (c == '0') ++cur;
				    else --cur;
				
			}
			out.println(ans);
		
		}
		
		out.close();
	}

	
}