import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/tmpl/citrus.nim
ImportExpand "cplib/tmpl/citrus" <=== "when not declared CPLIB_TMPL_CITRUS:\n    const CPLIB_TMPL_CITRUS* = 1\n    {.warning[UnusedImport]: off.}\n    {.hint[XDeclaredButNotUsed]: off.}\n    import os\n    import algorithm\n    import sequtils\n    import tables\n    import macros\n    import std/math\n    import sets\n    import strutils\n    import strformat\n    import sugar\n    import streams\n    import deques\n    import bitops\n    import heapqueue\n    import options\n    import hashes\n    const MODINT998244353* = 998244353\n    const MODINT1000000007* = 1000000007\n    when not declared CPLIB_UTILS_CONSTANTS:\n        const CPLIB_UTILS_CONSTANTS* = 1\n        const INF32*: int32 = 100100111.int32\n        const INF64*: int = int(3300300300300300491)\n    \n    const INFL = INF64\n    type double* = float64\n    let readNext = iterator(getsChar: bool = false): string {.closure.} =\n        while true:\n            var si: string\n            try: si = stdin.readLine\n            except EOFError: yield \"\"\n            for s in si.split:\n                if getsChar:\n                    for i in 0..<s.len():\n                        yield s[i..i]\n                else:\n                    if s.isEmptyOrWhitespace: continue\n                    yield s\n    proc input*(t: typedesc[string]): string = readNext()\n    proc input*(t: typedesc[char]): char = readNext(true)[0]\n    proc input*(t: typedesc[int]): int = readNext().parseInt\n    proc input*(t: typedesc[float]): float = readNext().parseFloat\n    macro input*(t: typedesc, n: varargs[int]): untyped =\n        var repStr = \"\"\n        for arg in n:\n            repStr &= &\"({arg.repr}).newSeqWith \"\n        parseExpr(&\"{repStr}input({t})\")\n    macro input*(ts: varargs[auto]): untyped =\n        var tupStr = \"\"\n        for t in ts:\n            tupStr &= &\"input({t.repr}),\"\n        parseExpr(&\"({tupStr})\")\n    macro input*(n: int, ts: varargs[auto]): untyped =\n        for typ in ts:\n            if typ.typeKind != ntyAnything:\n                error(\"Expected typedesc, got \" & typ.repr, typ)\n        parseExpr(&\"({n.repr}).newSeqWith input({ts.repr})\")\n    proc `fmtprint`*(x: int or string or char or bool): string = return $x\n    proc `fmtprint`*(x: float or float32 or float64): string = return &\"{x:.16f}\"\n    proc `fmtprint`*[T](x: seq[T] or Deque[T] or HashSet[T] or set[T]): string = return x.toSeq.join(\" \")\n    proc `fmtprint`*[T, N](x: array[T, N]): string = return x.toSeq.join(\" \")\n    proc `fmtprint`*[T](x: HeapQueue[T]): string =\n        var q = x\n        while q.len != 0:\n            result &= &\"{q.pop()}\"\n            if q.len != 0: result &= \" \"\n    proc `fmtprint`*[T](x: CountTable[T]): string =\n        result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n    proc `fmtprint`*[K, V](x: Table[K, V]): string =\n        result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n    proc print*(prop: tuple[f: File, sepc: string, endc: string, flush: bool], args: varargs[string, `fmtprint`]) =\n        for i in 0..<len(args):\n            prop.f.write(&\"{args[i]}\")\n            if i != len(args) - 1: prop.f.write(prop.sepc) else: prop.f.write(prop.endc)\n        if prop.flush: prop.f.flushFile()\n    proc print*(args: varargs[string, `fmtprint`]) = print((f: stdout, sepc: \" \", endc: \"\\n\", flush: false), args)\n    const LOCAL_DEBUG{.booldefine.} = false\n    macro getSymbolName(x: typed): string = x.toStrLit\n    macro debug*(args: varargs[untyped]): untyped =\n        when LOCAL_DEBUG:\n            result = newNimNode(nnkStmtList, args)\n            template prop(e: string = \"\"): untyped = (f: stderr, sepc: \"\", endc: e, flush: true)\n            for i, arg in args:\n                if arg.kind == nnkStrLit:\n                    result.add(quote do: print(prop(), \"\\\"\", `arg`, \"\\\"\"))\n                else:\n                    result.add(quote do: print(prop(\": \"), getSymbolName(`arg`)))\n                    result.add(quote do: print(prop(), `arg`))\n                if i != args.len - 1: result.add(quote do: print(prop(), \", \"))\n                else: result.add(quote do: print(prop(), \"\\n\"))\n        else:\n            return (quote do: discard)\n    proc `%`*(x: SomeInteger, y: SomeInteger): int =\n        result = x mod y\n        if y > 0 and result < 0: result += y\n        if y < 0 and result > 0: result += y\n    proc `//`*(x: SomeInteger, y: SomeInteger): int =\n        result = x div y\n        if y > 0 and result * y > x: result -= 1\n        if y < 0 and result * y < x: result -= 1\n    proc `^`*(x: SomeInteger, y: SomeInteger): int = x xor y\n    proc `&`*(x: SomeInteger, y: SomeInteger): int = x and y\n    proc `|`*(x: SomeInteger, y: SomeInteger): int = x or y\n    proc `>>`*(x: SomeInteger, y: SomeInteger): int = x shr y\n    proc `<<`*(x: SomeInteger, y: SomeInteger): int = x shl y\n    proc `%=`*(x: var SomeInteger, y: SomeInteger): void = x = x % y\n    proc `//=`*(x: var SomeInteger, y: SomeInteger): void = x = x // y\n    proc `^=`*(x: var SomeInteger, y: SomeInteger): void = x = x ^ y\n    proc `&=`*(x: var SomeInteger, y: SomeInteger): void = x = x & y\n    proc `|=`*(x: var SomeInteger, y: SomeInteger): void = x = x | y\n    proc `>>=`*(x: var SomeInteger, y: SomeInteger): void = x = x >> y\n    proc `<<=`*(x: var SomeInteger, y: SomeInteger): void = x = x << y\n    proc `[]`*(x, n: int): bool = (x and (1 shl n)) != 0\n    proc `[]=`*(x: var int, n: int, i: bool) =\n        if i: x = x or (1 << n)\n        else: (if x[n]: x = x xor (1 << n))\n    proc pow*(a, n: int, m = INF64): int =\n        var\n            rev = 1\n            a = a\n            n = n\n        while n > 0:\n            if n % 2 != 0: rev = (rev * a) mod m\n            if n > 1: a = (a * a) mod m\n            n >>= 1\n        return rev\n    when not declared CPLIB_MATH_ISQRT:\n        const CPLIB_MATH_ISQRT* = 1\n        proc isqrt*(n: int): int =\n            var x = n\n            var y = (x + 1) shr 1\n            while y < x:\n                x = y\n                y = (x + n div x) shr 1\n            return x\n    \n    proc chmax*[T](x: var T, y: T): bool {.discardable.} = (if x < y: (x = y; return true; ) return false)\n    proc chmin*[T](x: var T, y: T): bool {.discardable.} = (if x > y: (x = y; return true; ) return false)\n    proc `max=`*[T](x: var T, y: T) = x = max(x, y)\n    proc `min=`*[T](x: var T, y: T) = x = min(x, y)\n    proc at*(x: char, a = '0'): int = int(x) - int(a)\n    proc Yes*(b: bool = true): void = print(if b: \"Yes\" else: \"No\")\n    proc No*(b: bool = true): void = Yes(not b)\n    proc YES_upper*(b: bool = true): void = print(if b: \"YES\" else: \"NO\")\n    proc NO_upper*(b: bool = true): void = Yes_upper(not b)\n    const DXY* = [(0, -1), (0, 1), (-1, 0), (1, 0)]\n    const DDXY* = [(1, -1), (1, 0), (1, 1), (0, -1), (0, 1), (-1, -1), (-1, 0), (-1, 1)]\n    macro exit*(statement: untyped): untyped = (quote do: (`statement`; quit()))\n    proc initHashSet[T](): Hashset[T] = initHashSet[T](0)\n"
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/str/manachar.nim
ImportExpand "cplib/str/manachar" <=== "when not declared CPLIB_STR_MANACHAR:\n    const CPLIB_STR_MANACHAR* = 1\n    import sequtils\n    proc manachar*[T](s: seq[T]): seq[int] =\n        result = newSeq[int](s.len)\n        result[0] = 0\n        var c = 0\n        for i in 0..<s.len:\n            var l = 2*c - i\n            if l in 0..<s.len and i + result[l] < c + result[c]:\n                result[i] = result[l]\n            else:\n                var j = c + result[c] - i\n                while i-j >= 0 and i+j < s.len and s[i-j] == s[i+j]: j += 1\n                result[i] = j\n                c = i\n    proc manachar*(s: string): seq[int] = manachar(s.toSeq)\n"

# {.checks: off.}

proc solve() =
    var n,m = input(int)
    var s = input(string)
    proc insert_doller(s: string): string =
        result = ""
        for i in 0..<s.len:
            result &= s[i]
            if i != s.len - 1: result &= "$"
    if m <= 2*n:
        var s1 = insert_doller(s)
        var mc = manachar(s1)
        for i in 0..<mc.len:
            if i % 2 == 0:
                mc[i] = ((mc[i] + 1) // 2) * 2 - 1
            else:
                mc[i] //= 2
                mc[i] = (mc[i] * 2)
        debug(s1, mc)
        if mc.max >= m:
            print(1)
            return
        s1 = insert_doller(s & s)
        mc = manachar(s1)
        for i in 0..<mc.len:
            if i % 2 == 0:
                mc[i] = ((mc[i] + 1) // 2) * 2 - 1
            else:
                mc[i] //= 2
                mc[i] = (mc[i] * 2)
        debug(s1, mc)
        if mc.max >= m:
            print(2)
            return
        print(-1)
        return

    proc is_palindrome(s: string): bool = (s == s.reversed)
    if is_palindrome(s):
        print((m + n - 1) // n)
        return
    if is_palindrome(s[0..<n-1]) or is_palindrome(s[1..<n]):
        print((m + n) // n)
        return
    print(-1)
    return

var t = input(int)
for _ in 0..<t: solve()