There is a toy building consisting of n towers. Each tower consists of several cubes standing on each other. The i-th tower consists of h_i cubes, so it has height h_i.

Let's define operation slice on some height H as following: for each tower i, if its height is greater than H, then remove some top cubes to make tower's height equal to H. Cost of one "slice" equals to the total number of removed cubes from all towers.

Let's name slice as good one if its cost is lower or equal to k (k ≥ n).

<image>

Calculate the minimum number of good slices you have to do to make all towers have the same height. Of course, it is always possible to make it so.

Input

The first line contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, n ≤ k ≤ 10^9) — the number of towers and the restriction on slices, respectively.

The second line contains n space separated integers h_1, h_2, ..., h_n (1 ≤ h_i ≤ 2 ⋅ 10^5) — the initial heights of towers.

Output

Print one integer — the minimum number of good slices you have to do to make all towers have the same heigth.

Examples

Input

5 5
3 1 2 2 4


Output

2


Input

4 5
2 3 4 5


Output

2

Note

In the first example it's optimal to make 2 slices. The first slice is on height 2 (its cost is 3), and the second one is on height 1 (its cost is 4).
"""
What I cannot create, I do not understand.

https://github.com/Cheran-Senthil/PyRival
Copyright (c) 2018 Cheran Senthilkumar
"""
# IMPORTS---------------------------------------------------------------------#
from __future__ import division, print_function

import itertools
import sys
from atexit import register
from io import BytesIO

# import cmath
import math
# import operator as op
# import random
# from bisect import bisect, bisect_left
from collections import Counter, defaultdict, deque
# from copy import deepcopy
# from cPickle import dumps
# from decimal import Decimal, getcontext
# from difflib import SequenceMatcher
# from fractions import Fraction, gcd
# from heapq import heappop, heappush
# from Queue import PriorityQueue, Queue


# PYTHON3---------------------------------------------------------------------#
class dict(dict):
    def items(self):
        return dict.iteritems(self)

    def keys(self):
        return dict.iterkeys(self)

    def values(self):
        return dict.itervalues(self)


filter = itertools.ifilter
map = itertools.imap
zip = itertools.izip

input = raw_input
range = xrange


# FASTIO----------------------------------------------------------------------#
# sys.stdout = BytesIO()
# register(lambda: sys.__stdout__.write(sys.stdout.getvalue()))
# sys.stdin = BytesIO(sys.stdin.read())

# input = lambda: sys.stdin.readline().rstrip()
# print = lambda *args: sys.stdout.write(' '.join(str(x) for x in args) + '\n')
# flush = sys.stdout.flush


# SETTINGS--------------------------------------------------------------------#
# getcontext().prec = 100
# sys.setrecursionlimit(100000)


# CONSTANTS-------------------------------------------------------------------#
MOD = 1000000007
INF = float('+inf')

ASCII_LOWERCASE = 'abcdefghijklmnopqrstuvwxyz'
ASCII_UPPERCASE = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'


# MAIN------------------------------------------------------------------------#
def main():
    _, k = map(int, input().split(' '))
    h = Counter(map(int, input().split(' ')))
    ma, mi = max(h), min(h)
    tot, cnt = 0, 0
    slices = 0
    for i in range(ma, mi, -1):
        if i in h:
            tot += h[i]
        
        if cnt + tot > k:
            cnt = tot
            slices += 1
        elif cnt + tot == k:
            cnt = 0
            slices += 1
        else:
            cnt += tot

    if (ma == mi) or (cnt == 0):
        print(slices)
    else:
        print(slices + 1)
    


if __name__ == '__main__':
    main()
