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 inp():
    return (ss.rstrip() for ss in stdin).__next__()


def mpint():
    return map(int, inp().split())


def cnt(ss):
    return ss.count('0') * 2 - len(ss)


for case in range(int(inp())):
    n, x = mpint()
    s = inp()
    cnt = 0
    prefix = []
    for c in s:
        if c == '0':
            cnt += 1
        else:
            cnt -= 1
        prefix.append(cnt)

    if s[0] == '0':
        cnt += 1
    else:
        cnt -= 1
    cnt = cnt - prefix[0]

    ans = 1 if x == 0 else 0
    # print(prefix, cnt)
    if cnt == 0:
        if x in prefix:
            print(-1)
        else:
            print(ans)
    else:
        for k in prefix:
            if x == k or ((x - k) % cnt == 0 and (x - k) / cnt > 0):
                ans += 1
        print(ans)