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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
char s[100010];
int b[100010];
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    int n, x;
    scanf("%d%d%s", &n, &x, s);
    bool has_x = x == 0;
    b[0] = 0;
    for (int i = 1; i <= n; i++) {
      b[i] = b[i - 1] + (s[i - 1] == '0' ? 1 : -1);
      if (b[i] == x) has_x = true;
    }
    if (b[n] == 0) {
      printf("%d\n", has_x ? -1 : 0);
      continue;
    }
    int ans = 0;
    for (int i = 0; i < n; i++) {
      if ((x - b[i]) % b[n] == 0 and (x - b[i]) / b[n] >= 0) {
        ans++;
      }
    }
    printf("%d\n", ans);
  }
}