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
from math import log2,floor,ceil,sqrt
# import bisect
# from collections import deque

Ri = lambda : [int(x) for x in sys.stdin.readline().split()]
ri = lambda : sys.stdin.readline().strip()
 
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10 ** 18
MOD = 10**9+7

for _ in range(int(ri())):
    n,x = Ri()
    st = ri()
    # dic ={}
    pre = [0]*n
    cnt = 0
    if st[0] == '0':
        pre[0] = 1
    else:
        pre[0]  = -1
    # if pre[0] in dic:
    #         dic[pre[0]]+=1
    # else:
    #     dic[pre[0]] = 1
    if pre[0] == x:
        cnt+=1
    for i in range(1,len(st)):
        if st[i] == '1':
            pre[i] = pre[i-1]-1
        else:
            pre[i] = pre[i-1]+1
        # if pre[i] in dic:
        #     dic[pre[i]]+=1
        # else:
        #     dic[pre[i]] = 1
        if pre[i] == x:
            cnt+=1
    # print(pre)
    if pre[n-1] == 0:
        if cnt > 0:
            print(-1)
        else:
            print(0)
    else:
        if cnt == 0 and x == 0:
            print(1)
        else:
            last  = pre[n-1]
            ans = 0
            for i in pre:
                if((x-i) >= 0 and last >= 0) or ((x-i) <= 0 and last <= 0):
                    if (x-i) % last == 0:
                        ans+=1
            if x == 0:
                print(ans+1)
            else:
                print(ans)