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;
const long long INF = 571795717957;
const long long MOD = 1000000007;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long y = 0;
  cin >> y;
  while (y) {
    y--;
    long long n, x;
    cin >> n >> x;
    string binnum;
    cin >> binnum;
    vector<long long> pref = {};
    if (binnum[0] == '1') {
      pref.push_back(-1);
    } else {
      pref.push_back(1);
    }
    for (long long i = 1; i < n; i++) {
      if (binnum[i] == '1') {
        pref.push_back(pref.back() - 1);
      } else {
        pref.push_back(pref.back() + 1);
      }
    }
    long long f = 0;
    long long ending = pref.back();
    long long ans = 0;
    for (auto el : pref) {
      if (ending && (!((x - el) % ending)) && (x - el) / ending >= 0) {
        ans += 1;
      } else {
        if ((!ending) && (x == el) && (!f)) {
          cout << -1 << endl;
          f = 1;
        }
      }
    }
    if (!f) {
      if (x == 0) {
        cout << ans + 1 << endl;
      } else {
        cout << ans << endl;
      }
    }
  }
}