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 PYTHON3):

Solution:
''' Hey stalker :) '''
INF = 10**10
def main():
    print = out.append
    ''' Cook your dish here! '''
    n, x = get_list()
    prefix = [0]
    for i in input():
        if i=='0': prefix.append(prefix[-1] + 1)
        else: prefix.append(prefix[-1]-1)

    prefix = prefix[1:]
    #print(prefix)
    if prefix[-1]==0:
        if x in prefix:
            res = -1
        else: res = 0
    else:
        res = 0 if x!=0 else 1
        for i in prefix:
            if (x-i)%prefix[-1]==0 and (x-i)//prefix[-1]>=0: res += 1
    print(res)

''' Pythonista fLite 1.1 '''
import sys
#from collections import defaultdict, Counter
#from bisect import bisect_left, bisect_right
#from functools import reduce
import math
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
out = []
get_int = lambda: int(input())
get_list = lambda: list(map(int, input().split()))
#main()
[main() for _ in range(int(input()))]
print(*out, sep='\n')