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:
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#  (   |  |   |  (   |  (     (   |  |   |  (   |  (   |
# \__,_| _|  _| \__,_| \___| \___/  _|  _| \__,_| \__,_|

import sys
import math
import operator as op
from functools import reduce

def read_line():
	return sys.stdin.readline()[:-1]
 
def read_int():
	return int(sys.stdin.readline())
	
def read_int_line():
	return [int(v) for v in sys.stdin.readline().split()]

def read_float_line():
	return [float(v) for v in sys.stdin.readline().split()]

def ncr(n, r):
    r = min(r, n-r)
    numer = reduce(op.mul, range(n, n-r, -1), 1)
    denom = reduce(op.mul, range(1, r+1), 1)
    return numer / denom

t = read_int()
for i in range(t):
	n, x = read_int_line()
	s = read_line()
	
	p0 = [0]*n
	p1 = [0]*n
	
	if s[0] == "1":
		p1[0] = 1
	else:
		p0[0] = 1
	for i in range(1,n):
		if s[i] == "1":
			p1[i] = p1[i-1] + 1
			p0[i] = p0[i-1]
		else:
			p1[i] = p1[i-1]
			p0[i] = p0[i-1] + 1
			
	a = [0]*n
	for i in range(n):
		a[i] = p0[i] - p1[i]

	if a[-1]==0:
		ans = 0
		if x==0:
			ans+=1
		for i in range(n):
			if a[i]==x:
				ans+=1
		if ans>0:
			print(-1)
		else:
			print(0)
	else:
		ans = 0
		if x==0:
			ans+=1
		b = [(x-a[i])/a[n-1] for i in range(n)]
		for i in b:
			if i == int(i) and i>=0:
				ans+=1
		print(ans)