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:
import sys, array
t = int(input())
while t:
    n, x = map(int, sys.stdin.readline().split())
    s = sys.stdin.readline().replace("\n", "")
    a = array.array("i", range(n)) 
    cz = 0
    co = 0 
    ans = 0
    for i in range(n):
        if s[i] == "0":
            cz += 1
            a[i] = cz - co
        else:
            co += 1
            a[i] = cz - co
    if x == 0:
        if a[n-1] == 0:
            ans = -1
        elif a[n-1] > 0:
            for each in a:
                if each == 0 or (each < 0 and abs(each) % a[n-1] == 0):
                    ans += 1
        elif a[n-1] < 0:
            for each in a:
                if each == 0 or (each > 0 and abs(each) % abs(a[n-1]) == 0):
                    ans += 1
        if ans >= 0:
            ans += 1
    else:
        if a[n-1] == 0:
            if x in a:
                ans = -1
            else:
                ans = 0
        elif a[n-1] > 0:
            for each in a:
                if each == x or (each < x and (x - each) % abs(a[n-1]) == 0):
                    ans += 1
        else:
            for each in a:
                if each == x or (each > x and (each - x) % abs(a[n-1]) == 0):
                    ans += 1
    print(ans)
    t -= 1