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
input = sys.stdin.readline
from collections import Counter

t=int(input())

for test in range(t):
    n,x=map(int,input().split())
    s=input().strip()

    Z=[0]
    for st in s:
        if st=="0":
            Z.append(Z[-1]+1)
        else:
            Z.append(Z[-1]-1)

    Z=Z[1:]
    C=Counter(Z)

    #print(Z)

    change=Z[-1]
    MAX=max(Z)
    MIN=min(Z)

    if change==0 and MIN<=x<=MAX:
        print(-1)
        continue
    elif change==0:
        print(0)
        continue

    #print(-(-(x-MAX)//change),(x-MIN)//change)

    if x==0:
        ANS=1
    else:
        ANS=0

    if change>0:
        
        for i in range(max(0,(x-MAX)//change-2),(x-MIN)//change+2):
            ANS+=C[x-change*i]

    else:
        for i in range(max(0,(x-MIN)//change-2),(x-MAX)//change+2):
            ANS+=C[x-change*i]
        

    print(ANS)