# taken from https://tjkendev.github.io/procon-library/python/string/manacher.html
def manacher(S):
	C = []
	for a in S:
		C.append(a)
		C.append(0)
	C.pop()
	L = len(C)
	R = [0]*L
	i = j = 0
	while i < L:
		while j <= i < L-j and C[i-j] == C[i+j]:
			j += 1
		R[i] = j
		k = 1
		while j-R[i-k] > k <= i < L-k:
			R[i+k] = R[i-k]
			k += 1
		i += k; j -= k
	for i in range(L):
		if i & 1 == R[i] & 1:
			R[i] -= 1
	return R

def longest_palindrome(s):
	return max(manacher(s))

def solve(n, m, s):
	v1 = longest_palindrome(s * 1)
	v2 = longest_palindrome(s * 2)
	v3 = longest_palindrome(s * 3)
	v4 = longest_palindrome(s * 4)
	if v1 >= m:
		return 1
	if v2 >= m:
		return 2
	if v3 >= m:
		return 3
	ans = -1
	if v3 >= 2 * n:
		subans = 3 + (m - v3 + 2 * n - 1) // (2 * n) * 2
		ans = (subans if ans == -1 else min(ans, subans))
	if v4 >= 2 * n:
		subans = 4 + (m - v4 + 2 * n - 1) // (2 * n) * 2
		ans = (subans if ans == -1 else min(ans, subans))
	return ans

t = int(input())
for _ in range(t):
	n, m = map(int, input().split())
	s = input()
	print(solve(n, m, s))