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:
from sys import stdin


def input():
    return stdin.readline()[:-1]


def intput():
    return int(input())


def sinput():
    return input().split()


def intsput():
    return map(int, sinput())


debugging = False
def dprint(*args):
    if debugging:
        print(*args)
    else:
        pass



shift = 100001
# Code
t = intput()
for _ in range(t):
    n, x = intsput()

    s = input()

    balances = [0] * 200002

    b = 0
    for i in range(n):
        if s[i] == '1':
            b -= 1
        else:
            b += 1
        balances[b + shift] += 1

    
    finalb = b
    if finalb == 0 and 0 <= x + shift < len(balances) and balances[x + shift]:
        print(-1)
        continue
    elif finalb == 0:
        print(0)
        continue

    k = x
    ans = 0
    if x == 0:
        ans += 1

    if len(balances) > k + shift >= 0:
        while len(balances) > k + shift >= 0:
            ans += balances[k + shift]
            k -= finalb
        print(ans)
    else:
        if k + shift >= len(balances) and finalb > 0:
            k -= (((k + shift) - len(balances) + 1) // finalb) * finalb
            while k + shift >= len(balances):
                k -= finalb
            while len(balances) > k + shift >= 0:
                ans += balances[k + shift]
                k -= finalb
            print(ans)
        elif k + shift < 0 and finalb < 0:
            k += ((0 - (k + shift)) // (-finalb)) * (-finalb)
            while k + shift < 0:
                k += - finalb
            while len(balances) > k + shift >= 0:
                ans += balances[k + shift]
                k -= finalb
            print(ans)
        else:
            print(0)