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.*;
import java.math.*;
 
public class Solution {
	static final long mod = (long)1e9+7;
	public static void main (String[] args) {
	    FastScanner sc = new FastScanner(System.in);
		int t = sc.nextInt();
		while(t-->0){
		    int n = sc.nextInt();
		    int x = sc.nextInt();
		    String s = sc.nextLine();
		    int[] cnt = new int[n];
		    if(s.charAt(0)=='0') cnt[0] = 1;
		    else cnt[0] = -1;
		    for(int i=1;i<n;i++){
		        cnt[i]=cnt[i-1]+(s.charAt(i)=='0' ? 1 : -1);
		    }
		    boolean ok = true;
		    long ans = 0;
		    int diff = cnt[n-1];
		    for(int i=0;i<n;i++){
		        if(diff==0 && cnt[i]==x){
		            ok = false;
		            break;
		        }
		        if(cnt[i]==x) {
		            ans++;
		            continue;
		        }
		        if(diff==0) {
		            continue;
		        }
		        if(diff>0 && cnt[i]>x) continue;
		        if(diff<0 && cnt[i]<x) continue;
		        if((x-cnt[i])%diff == 0) ans++;
		    }
		    if(!ok){
		        System.out.println(-1);
		        continue;
		    }
		    if(x==0) ans++;
		    System.out.println(ans);
		}
	}
	static long[][] mul(long[][] a, long[][] b){
	    long[][] c = new long[a.length][b[0].length];
	    for(int i=0;i<a.length;i++){
	        for(int j=0;j<b[0].length;j++){
	            for(int k=0;k<b.length;k++){
	                c[i][j] = (c[i][j]+(a[i][k]*b[k][j])%mod)%mod;
	            }
	        }
	    }
	    return c;
	}
	static long[][] pow(long[][] a, long n){
	    if(n==1) return a;
	    long[][] c = pow(a, n/2);
	    c = mul(c, c);
	    if(n%2==1) c = mul(c, a);
	    return c;
	}
	static class Pair{
	    int a, b;
	    public Pair(int c, int d){
	        a = c;
	        b = d;
	    }
	}
	static long power(long a, long b, long c){
	    if(b==0) return 1L;
	    if(b==1) return a;
	    long temp = power(a, b/2, c);
	    if(b%2==0) return (temp*temp)%c;
	    else return (((temp*temp)%c)*a)%c;
	}
	// l = -1, r = len-1
	static int CeilIndex(int A[], int l, int r, int key) {
        while (r - l > 1) { 
            int m = l + (r - l) / 2; 
            if (A[m] >= key) 
                r = m; 
            else
                l = m; 
        }
        if(r>=0 && A[r]<key) return -1;
        return r; 
    }
    static int floorIndex(int A[], int l, int r, int key) {
        while (r - l > 1) { 
            int m = l + (r - l) / 2; 
            if (A[m] <= key) 
                r = m; 
            else
                l = m; 
        } 
        return l; 
    }
	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}
		FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}
		String nextLine() {
			try {
				return br.readLine();
			} catch (IOException e) {
				return null;
			}
		}
		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}