The only difference between the easy and the hard versions is constraints.

A subsequence is a string that can be derived from another string by deleting some or no symbols without changing the order of the remaining symbols. Characters to be deleted are not required to go successively, there can be any gaps between them. For example, for the string "abaca" the following strings are subsequences: "abaca", "aba", "aaa", "a" and "" (empty string). But the following strings are not subsequences: "aabaca", "cb" and "bcaa".

You are given a string s consisting of n lowercase Latin letters.

In one move you can take any subsequence t of the given string and add it to the set S. The set S can't contain duplicates. This move costs n - |t|, where |t| is the length of the added subsequence (i.e. the price equals to the number of the deleted characters).

Your task is to find out the minimum possible total cost to obtain a set S of size k or report that it is impossible to do so.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 100, 1 ≤ k ≤ 10^{12}) — the length of the string and the size of the set, correspondingly.

The second line of the input contains a string s consisting of n lowercase Latin letters.

Output

Print one integer — if it is impossible to obtain the set S of size k, print -1. Otherwise, print the minimum possible total cost to do it.

Examples

Input


4 5
asdf


Output


4


Input


5 6
aaaaa


Output


15


Input


5 7
aaaaa


Output


-1


Input


10 100
ajihiushda


Output


233

Note

In the first example we can generate S = { "asdf", "asd", "adf", "asf", "sdf" }. The cost of the first element in S is 0 and the cost of the others is 1. So the total cost of S is 4.
# ---------------------------iye ha aam zindegi---------------------------------------------
import math
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
mod = 10 ** 9 + 7
mod1 = 998244353
#setrecursionlimit(300000)
# ------------------------------warmup----------------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
sys.setrecursionlimit(300000)
class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")


# -------------------game starts now----------------------------------------------------import math
class SegmentTree:
    def __init__(self, data, default=0, func=lambda a, b: a + b):
        """initialize the segment tree with data"""
        self._default = default
        self._func = func
        self._len = len(data)
        self._size = _size = 1 << (self._len - 1).bit_length()

        self.data = [default] * (2 * _size)
        self.data[_size:_size + self._len] = data
        for i in reversed(range(_size)):
            self.data[i] = func(self.data[i + i], self.data[i + i + 1])

    def __delitem__(self, idx):
        self[idx] = self._default

    def __getitem__(self, idx):
        return self.data[idx + self._size]

    def __setitem__(self, idx, value):
        idx += self._size
        self.data[idx] = value
        idx >>= 1
        while idx:
            self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
            idx >>= 1

    def __len__(self):
        return self._len

    def query(self, start, stop):
        if start == stop:
            return self.__getitem__(start)
        stop += 1
        start += self._size
        stop += self._size

        res = self._default
        while start < stop:
            if start & 1:
                res = self._func(res, self.data[start])
                start += 1
            if stop & 1:
                stop -= 1
                res = self._func(res, self.data[stop])
            start >>= 1
            stop >>= 1
        return res

    def __repr__(self):
        return "SegmentTree({0})".format(self.data)


# -------------------------------iye ha chutiya zindegi-------------------------------------
class Factorial:
    def __init__(self, MOD):
        self.MOD = MOD
        self.factorials = [1, 1]
        self.invModulos = [0, 1]
        self.invFactorial_ = [1, 1]

    def calc(self, n):
        if n <= -1:
            print("Invalid argument to calculate n!")
            print("n must be non-negative value. But the argument was " + str(n))
            exit()
        if n < len(self.factorials):
            return self.factorials[n]
        nextArr = [0] * (n + 1 - len(self.factorials))
        initialI = len(self.factorials)
        prev = self.factorials[-1]
        m = self.MOD
        for i in range(initialI, n + 1):
            prev = nextArr[i - initialI] = prev * i % m
        self.factorials += nextArr
        return self.factorials[n]

    def inv(self, n):
        if n <= -1:
            print("Invalid argument to calculate n^(-1)")
            print("n must be non-negative value. But the argument was " + str(n))
            exit()
        p = self.MOD
        pi = n % p
        if pi < len(self.invModulos):
            return self.invModulos[pi]
        nextArr = [0] * (n + 1 - len(self.invModulos))
        initialI = len(self.invModulos)
        for i in range(initialI, min(p, n + 1)):
            next = -self.invModulos[p % i] * (p // i) % p
            self.invModulos.append(next)
        return self.invModulos[pi]

    def invFactorial(self, n):
        if n <= -1:
            print("Invalid argument to calculate (n^(-1))!")
            print("n must be non-negative value. But the argument was " + str(n))
            exit()
        if n < len(self.invFactorial_):
            return self.invFactorial_[n]
        self.inv(n)  # To make sure already calculated n^-1
        nextArr = [0] * (n + 1 - len(self.invFactorial_))
        initialI = len(self.invFactorial_)
        prev = self.invFactorial_[-1]
        p = self.MOD
        for i in range(initialI, n + 1):
            prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p
        self.invFactorial_ += nextArr
        return self.invFactorial_[n]


class Combination:
    def __init__(self, MOD):
        self.MOD = MOD
        self.factorial = Factorial(MOD)

    def ncr(self, n, k):
        if k < 0 or n < k:
            return 0
        k = min(k, n - k)
        f = self.factorial
        return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD


# --------------------------------------iye ha combinations ka zindegi---------------------------------
def powm(a, n, m):
    if a == 1 or n == 0:
        return 1
    if n % 2 == 0:
        s = powm(a, n // 2, m)
        return s * s % m
    else:
        return a * powm(a, n - 1, m) % m


# --------------------------------------iye ha power ka zindegi---------------------------------
def sort_list(list1, list2):
    zipped_pairs = zip(list2, list1)

    z = [x for _, x in sorted(zipped_pairs)]

    return z


# --------------------------------------------------product----------------------------------------
def product(l):
    por = 1
    for i in range(len(l)):
        por *= l[i]
    return por


# --------------------------------------------------binary----------------------------------------
def binarySearchCount(arr, n, key):
    left = 0
    right = n - 1

    count = 0

    while (left <= right):
        mid = int((right + left) / 2)

        # Check if middle element is
        # less than or equal to key
        if (arr[mid] < key):
            count = mid + 1
            left = mid + 1

        # If key is smaller, ignore right half
        else:
            right = mid - 1

    return count


# --------------------------------------------------binary----------------------------------------
def countdig(n):
    c = 0
    while (n > 0):
        n //= 10
        c += 1
    return c
def binary(x, length):
    y = bin(x)[2:]
    return y if len(y) >= length else "0" * (length - len(y)) + y

def countGreater(arr, n, k):
    l = 0
    r = n - 1

    # Stores the index of the left most element
    # from the array which is greater than k
    leftGreater = n

    # Finds number of elements greater than k
    while (l <= r):
        m = int(l + (r - l) / 2)
        if (arr[m] >= k):
            leftGreater = m
            r = m - 1

        # If mid element is less than
        # or equal to k update l
        else:
            l = m + 1

    # Return the count of elements
    # greater than k
    return (n - leftGreater)


# --------------------------------------------------binary------------------------------------
class BinaryTrie:
    class Node:
        def __init__(self, bit: bool = False):
            self.bit = bit  # Stores the current bit (False if 0, True if 1)
            self.children = []
            self.count = 0  # stores number of keys finishing at this bit
            self.counter = 1  # stores number of keys with this bit as prefix

    def __init__(self, size):
        self.root = BinaryTrie.Node()
        self.size = size  # Maximum size of each key

    def convert(self, key):
        """Converts key from string/integer to a list of boolean values!"""
        bits = []
        if isinstance(key, int):
            key = bin(key)[2:]
        if isinstance(key, str):
            for i in range(self.size - len(key)):
                bits += [False]
            for i in key:
                if i == "0":
                    bits += [False]
                else:
                    bits += [True]
        else:
            return list(key)
        return bits

    def add(self, key):
        """Add a key to the trie!"""
        node = self.root
        bits = self.convert(key)
        for bit in bits:
            found_in_child = False
            for child in node.children:
                if child.bit == bit:
                    child.counter += 1
                    node = child
                    found_in_child = True
                    break
            if not found_in_child:
                new_node = BinaryTrie.Node(bit)
                node.children.append(new_node)
                node = new_node
        node.count += 1

    def remove(self, key):
        """Removes a key from the trie! If there are multiple occurences, it removes only one of them."""
        node = self.root
        bits = self.convert(key)
        nodelist = [node]
        for bit in bits:
            for child in node.children:
                if child.bit == bit:
                    node = child
                    node.counter -= 1
                    nodelist.append(node)
                    break
        node.count -= 1
        if not node.children and not node.count:
            for i in range(len(nodelist) - 2, -1, -1):
                nodelist[i].children.remove(nodelist[i + 1])
                if nodelist[i].children or nodelist[i].count:
                    break

    def query(self, prefix, root=None):
        """Search for a prefix in the trie! Returns the node if found, otherwise 0."""
        if not root: root = self.root
        node = root
        if not root.children:
            return 0
        for bit in prefix:
            bit_not_found = True
            for child in node.children:
                if child.bit == bit:
                    bit_not_found = False
                    node = child
                    break
            if bit_not_found:
                return 0
        return node
#--------------------------------------------trie-------------------------------------------------
class TrieNode:

    # Trie node class
    def __init__(self):
        self.children = [None] * 26
        self.data=0
        self.isEndOfWord = False


class Trie:

    # Trie data structure class
    def __init__(self):
        self.root = self.getNode()

    def getNode(self):

        # Returns new trie node (initialized to NULLs)
        return TrieNode()

    def _charToIndex(self, ch):

        # private helper function
        # Converts key current character into index
        # use only 'a' through 'z' and lower case

        return ord(ch) - ord('a')

    def insert(self, key,val):
        pCrawl = self.root
        length = len(key)
        for level in range(length):
            index = self._charToIndex(key[level])

            # if current character is not present
            if not pCrawl.children[index]:
                pCrawl.children[index] = self.getNode()
            pCrawl = pCrawl.children[index]
            pCrawl.data+=val
        pCrawl.isEndOfWord = True

    def search(self, key):

        # Search key in the trie
        # Returns true if key presents
        # in trie, else false
        pCrawl = self.root
        length = len(key)
        c=0
        for level in range(length):
            index = self._charToIndex(key[level])
            if not pCrawl.children[index]:
                return False
            pCrawl = pCrawl.children[index]
        return pCrawl!=None
    def present(self, key):
        ans=0
        pCrawl = self.root
        length = len(key)
        c=0
        for level in range(length):
            index = self._charToIndex(key[level])
            if not pCrawl.children[index]:
                return False
            pCrawl = pCrawl.children[index]
            ans+=pCrawl.data
        if pCrawl!=None:
            return ans
        return -1
#----------------------------------trie----------------------------
n,k=map(int,input().split())
s=input()
last=defaultdict(int)
dp=[[0 for i in range(n+1)]for j in range(n+1)]
dp[0][0]=1
dp[1][1]=1
dp[1][0]=1
last[s[0]]=1
for i in range(2,n+1):
    dp[i][0]=1
    #print(last[s[i-1]])
    for j in range(1,i+1):
        dp[i][j]=dp[i-1][j-1]+dp[i-1][j]
        #print(dp[i][j],i,j)
        if last[s[i-1]]>=1:
            ind=last[s[i-1]]
            dp[i][j]-=dp[ind-1][j-1]
            #print(dp[ind-1][j-1],"JJKJJK",dp[i][j])
    last[s[i-1]]=i
ans=0
for i in range(n,-1,-1):
    if k<=0:
        break
    c=min(dp[n][i],k)
    ans+=(n-i)*c
    k-=c
if k>0:
    ans=-1
print(ans)
