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:
# Contest: Educational Codeforces Round 81 (Rated for Div. 2) (https://codeforces.com/contest/1295)
# Problem: B: Infinite Prefixes (https://codeforces.com/contest/1295/problem/B)

def rint():
    return int(input())


def rints():
    return list(map(int, input().split()))


t = rint()
for _ in range(t):
    n, x = rints()
    s = input()
    bal, min_bal, max_bal = 0, 0, 0
    from collections import defaultdict
    counts = defaultdict(int)
    for c in s:
        bal += 1 if c == '0' else -1
        min_bal = min(min_bal, bal)
        max_bal = max(max_bal, bal)
        counts[bal] += 1
    bal_range = max_bal - min_bal
    if bal == 0:
        if min_bal <= x <= max_bal:
            print(-1)
        else:
            print(0)
    else:
        b = 0
        d = 1 if x == 0 else 0
        for c in s:
            b += 1 if c == '0' else -1
            d += (x - b) % bal == 0 and (x - b) // bal >= 0
        print(d)