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;
using datatype = long;
int main() {
  std::ios::sync_with_stdio(false);
  int N;
  cin >> N;
  unordered_map<datatype, datatype> mp;
  for (int i = 0; i < N; ++i) {
    datatype sz, target;
    cin >> sz >> target;
    string nums;
    std::getline(cin, nums);
    mp.clear();
    datatype delta{0};
    for (size_t i = 0; i < sz; ++i) {
      char ch;
      cin >> ch;
      if (ch == '0')
        delta++;
      else
        delta--;
      mp[delta]++;
    }
    datatype count{0};
    if (target == 0)
      if (delta == 0)
        count = -1;
      else {
        count = 1;
        for (const auto& el : mp) {
          auto rw = target - el.first;
          if (rw / delta >= 0 && rw % delta == 0) count += el.second;
        }
      }
    else if (delta == 0) {
      if (mp[target] != 0)
        count = -1;
      else
        count = 0;
    } else {
      for (const auto& el : mp) {
        auto rw = target - el.first;
        if (rw / delta >= 0 && rw % delta == 0) count += el.second;
      }
    }
    cout << count << endl;
  }
  return 0;
}