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 PYTHON):

Solution:
from collections import Counter, defaultdict, deque
import itertools
import bisect
from sys import stdin, stdout
from itertools import repeat
import sys


# sys.stdin = open('input')
# sys.stdout = open('/mnt/d/Gg/output', 'w')
# n, k = map(int, raw_input().split())
# da = map(int, raw_input().split())
# db = map(int, raw_input().split())



def main():
    q = map(int, raw_input().split())[0]
    for _ in range(q):
        n, x = map(int, raw_input().split())
        st = raw_input().strip()
        n0, n1 = 0, 0
        total = len(st)
        for idx, c in enumerate(st):
            if c=='1':
                n1+=1
            else:
                n0+=1
        f_diff = n0-n1
        ans = 0
        n0, n1 = 0, 0
        if x==0:
            ans += 1
        for idx, c in enumerate(st):
            if c=='1':
                n1+=1
            else:
                n0+=1
            diff = n0-n1
            ta = x - diff
            if f_diff==0:
                if ta==0:
                    print -1
                    break
                else:
                    continue
            if ta*f_diff>=0 and ta%f_diff==0:
                ans += 1
                # print idx, c, ta, diff
        else:
            print ans




# import time
# pre = time.time()
main()