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:
bestNum = {2: 1, 3: 7, 4: 7, 5: 7, 6: 9, 7: 9}

ans = []
for t in range(int(input())):
	n, x = [int(i) for i in input().split()]
	s = input()
	currBal = 0
	pSum = []
	for i in s:
		if i == '0':
			currBal += 1
		else:
			currBal -= 1
		pSum.append(currBal)

	count = 0
	n -= 1
	if pSum[n] != 0:
		l = 0
		for i in pSum:
			temp = (x - i)
			div = temp % pSum[n]
			if temp == 0 or (pSum[n] > 0 and temp > 0 and div == 0) or (pSum[n] < 0 and temp < 0 and div == 0):
				# print(l, "index ke liye")
				count += 1
			l += 1
	else:
		for i in pSum:
			temp = (x - i)
			if temp == 0:
				# print(i - 1, "index ke liye")
				count += 1

	a = count
	if a > 0 and pSum[n] == 0:
		a = -1
	elif x == 0:
		a += 1
	ans.append(str(a))
print('\n'.join(ans))