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;
void iter() {
  int n, x;
  cin >> n >> x;
  int bals[n + 1];
  string s;
  cin >> s;
  bals[0] = 0;
  for (int j = 1; j <= n; j++) {
    int diff = 2 * (s[j - 1] == '0') - 1;
    bals[j] = bals[j - 1] + diff;
  }
  int last_bal = bals[n];
  if (last_bal == 0) {
    bool exists = false;
    for (int bal : bals) {
      if (x == bal) exists = true;
    }
    if (exists) {
      cout << -1 << endl;
    } else {
      cout << 0 << endl;
    }
  } else {
    int total = 0;
    for (int j = 0; j <= n - 1; j++) {
      int bal = bals[j];
      if (((x - bal) % last_bal) == 0 && ((x - bal) / last_bal) >= 0) {
        total++;
      }
    }
    cout << total << endl;
  }
}
int main() {
  int t;
  cin >> t;
  for (int i = 1; i <= t; i++) {
    iter();
  }
  return 0;
}