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[100005];
int pre[100005];
map<int, int> pmap;
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n, x;
    scanf("%d%d%s", &n, &x, s);
    pmap.clear();
    int pref = 0;
    for (int i = 0; i < n; i++) {
      if (s[i] == '0')
        pref++;
      else
        pref--;
      pre[i] = pref;
      pmap[pre[i]]++;
    }
    if (pref == 0 && pmap.find(x) != pmap.end())
      printf("-1\n");
    else {
      long long ans = 0;
      int rpre = pmap.rbegin()->first;
      int lpre = pmap.begin()->first;
      if (x < lpre) {
        if (pref < 0) {
          int k = (x - lpre) / pref;
          if ((lpre - x) % (-pref)) k++;
          int focus = x - (k * pref);
          while (focus >= lpre && focus <= rpre) {
            ans += pmap[focus];
            focus -= pref;
          }
        }
      } else if (x > rpre) {
        if (pref > 0) {
          int k = (x - rpre) / pref;
          if ((x - rpre) % pref) k++;
          int focus = x - (k * pref);
          while (focus >= lpre && focus <= rpre) {
            ans += pmap[focus];
            focus -= pref;
          }
        }
      } else if (pref != 0) {
        int focus = x;
        while (focus >= lpre && focus <= rpre) {
          ans += pmap[focus];
          focus -= pref;
        }
      }
      if (x == 0) ans++;
      printf("%lld\n", ans);
    }
  }
  return 0;
}