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:
import sys
import math
 
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()]

t = read_int()

for i in range(t):
	n,x = read_int_line()
	s = read_line()

	l = [0 for i in range(n)]

	if s[0]=="0":
		l[0] = 1
	else:
		l[0] = -1

	cnt = 0

	for i in range(1,n):
		# if l[i]==x:
		# 	cnt+=1
		if s[i]=="1":
			l[i]=l[i-1]-1
		else:
			l[i]=l[i-1]+1

	f = False
	for i in range(n):
		if x-l[i]==0 and l[n-1]==0:
			f = True

	if not f and l[n-1]!=0:
		for j in range(n):
			if (x-l[j])%l[n-1] == 0:
				if ((x-l[j])//l[n-1])*n + j+1 >= 0:
					cnt+=1
		
		print(cnt)

	elif not f and l[n-1]==0:
		print(0)

	else:
		print(-1)