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:
t = int(input().strip())
for _ in range(t):
    n,x = map(int,input().strip().split())
    s = input().strip()
    #1 balance == 0
    the_max,the_min,cur = -100010,100010,0
    cost = dict()
    for index,i in enumerate(s,1):
        if i == '1':
            cur -= 1
            if cur < the_min:
                the_min = cur
        else:
            cur += 1
            if cur > the_max:
                the_max = cur
        cost[index] = cur
    if cur == 0:
        if x == 0:
            print(-1)
        elif x > 0:
            if the_max >= x:
                print(-1)
            else:
                print(0)
        else:
            if the_min <= x:
                print(-1)
            else:
                print(0)
    else:
        ans = (1 if x == 0 else 0)
        for i in range(1,n + 1):
            re = x - cost[i]
            if re//cur >= 0 and re%cur == 0:
                ans += 1
        print(ans)