#![allow(unused_imports)]

fn main() {
    input! {
        t: usize,
    }
    for _ in 0..t {
        input! {
            n: usize, m: usize,
            s: Chars,
        }
        let mut t = s.clone();
        t.reverse();
        if s == t {
            // include n == 1
            println!("{}", (m + n - 1) / n);
            continue;
        }
        // then n >= 2
        if s[..n - 1] == t[1..] || s[1..] == t[..n - 1] {
            // a[pal] or [pal]a
            // concat k times a[pal] => a[pal]a[pal]..a[pal]
            // longest length [pal]a[pal]..a[pal], n*k-1
            // n*k-1 >= m
            println!("{}", (m + 1 + n - 1) / n);
            continue;
        }
        println!("-1");
    }
}

/*
useuseuse
abababa
abaabaaba
abcdcbabcdcbabcdcbabcdcb
abcdcabcdcabcdcabcdcabcdc
*/

use proconio::{input, marker::*};
use std::{cmp::Reverse, collections::*};

#[macro_export]
macro_rules! chmax {
    ($a:expr, $b:expr) => {{
        let tmp = $b;
        if $a < tmp {
            $a = tmp;
            true
        } else {
            false
        }
    }};
}

#[macro_export]
macro_rules! chmin {
    ($a:expr, $b:expr) => {{
        let tmp = $b;
        if $a > tmp {
            $a = tmp;
            true
        } else {
            false
        }
    }};
}

#[macro_export]
/// mvec![]
macro_rules! mvec {
    ($val:expr; ()) => {
        $val
    };
    ($val:expr; ($size:expr $(,$rest:expr)*)) => {
        vec![mvec![$val; ($($rest),*)]; $size]
    };
}