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:
#!/usr/bin/env python3
import os
import sys
from atexit import register
from io import StringIO

# Buffered output, at least 2x faster.
sys.stdout = StringIO()
register(lambda: os.write(1, sys.stdout.getvalue().encode()))

def sign(n):
    if n > 0:
        return 1
    elif n < 0:
        return -1
    else:
        return 0

###############################################################################

T = int(input())
for _ in range(T):
    [n,x] = [int(k) for k in input().split()]
    s = input()

    balances = {}
    b = 0
    for c in s:
        b += 1 if c == "0" else -1
        if b not in balances:
            balances[b] = 0
        balances[b] += 1

    if b == 0:
        print(-1 if x in balances else 0)
    else:
        ret = 0
        if x == 0:
            ret += 1
        for k in balances:
            if (x - k) % b == 0 and sign(x-k) == sign(b):
                ret += balances[k]
            elif x == k:
                ret += balances[k]
        print(ret)