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>
#pragma GCC optimizer(2)
using namespace std;
const int INF = 0x3f3f3f3f;
const int M = 40005;
const int N = 95;
int main() {
  long long t, n, x, a[100100], len, flag;
  cin >> t;
  char s[100010];
  while (t--) {
    cin >> n >> x;
    long long cnt0, cnt1, cnt;
    scanf("%s", s);
    len = strlen(s);
    cnt1 = cnt0 = cnt = flag = 0;
    a[0] = 0;
    for (int i = 1; i <= len; i++) {
      if (s[i - 1] == '0')
        cnt0++;
      else
        cnt1++;
      a[i] = cnt0 - cnt1;
      if (a[i] == x) flag = 1;
    }
    if ((!a[len] && flag)) {
      cout << "-1" << endl;
      continue;
    }
    long long tmp;
    if (!x) cnt++;
    for (int i = 1; i <= len; i++) {
      tmp = x - a[i];
      if (!tmp) cnt++;
      if (a[len] && !(tmp % a[len]) && (a[len] * tmp > 0)) cnt++;
    }
    cout << cnt << endl;
  }
  return 0;
}