Problem:
Score : 400 points

Problem Statement

You have N items and a bag of strength W.
The i-th item has a weight of w_i and a value of v_i.

You will select some of the items and put them in the bag.
Here, the total weight of the selected items needs to be at most W.

Your objective is to maximize the total value of the selected items.

Constraints

1 ≤ N ≤ 100

1 ≤ W ≤ 10^9

1 ≤ w_i ≤ 10^9

For each i = 2,3,...,N, w_1 ≤ w_i ≤ w_1 + 3.

1 ≤ v_i ≤ 10^7

W, each w_i and v_i are integers.

Input

Input is given from Standard Input in the following format:

N W
w_1 v_1
w_2 v_2
:
w_N v_N

Output

Print the maximum possible total value of the selected items.

Sample Input 1

4 6
2 1
3 4
4 10
3 4

Sample Output 1

11

The first and third items should be selected.

Sample Input 2

4 6
2 1
3 7
4 10
3 6

Sample Output 2

13

The second and fourth items should be selected.

Sample Input 3

4 10
1 100
1 100
1 100
1 100

Sample Output 3

400

You can take everything.

Sample Input 4

4 1
10 100
10 100
10 100
10 100

Sample Output 4

0

You can take nothing.

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

require 'prime'
include Math
def max(a,b);              a > b ? a : b                              end
def min(a,b);              a < b ?  a : b                             end
def swap(a,b);             a, b = b, a                                end
def gif;                   gets.to_i                                  end
def gff;                   gets.to_f                                  end
def gsf;                   gets.chomp                                 end
def gi;                    gets.split.map(&:to_i)                     end
def gf;                    gets.split.map(&:to_f)                     end
def gs;                    gets.chomp.split.map(&:to_s)               end
def gc;                    gets.chomp.split('')                       end
def pr(num);               num.prime_division                         end
def digit(num);            num.to_s.length                            end
def array(s,ini=nil);      Array.new(s){ini}                          end
def darray(s1,s2,ini=nil); Array.new(s1){Array.new(s2){ini}}          end
def rep(num);              num.times{|i|yield(i)}                     end
def repl(st,en,n=1);       st.step(en,n){|i|yield(i)}                 end



$n,$w = gi
$wv = []
rep $n do
	$wv << gi
end
$dp = darray $w+1,2,0
$wv.sort!
R = RubyVM::InstructionSequence
R.compile_option = {tailcall_optimization: true, trace_instruction: false}
R.new(<<~EOS).eval
def f jd, data,weight,i
	if $dp[weight][1] == 1
		if $dp[weight][0] < data
			$dp[weight][0] = data
		end
		return $dp[weight][0] 
	end
	if weight == $w || i == $n
		return data 
	end
	if jd == 0
		d = max f(1,data,weight,i+1), f(0,data,weight,i+1)
		if $dp[weight][0] < d
			$dp[weight][0] = d
			$dp[weight][1] = 1
		end
		return d
	else
		ww = weight+$wv[i][0]
		return data if ww > $w
		d = max f(1,data+$wv[i][1],ww,i+1),f(0,data+$wv[i][1],ww,i+1)
		if $dp[ww][0] < d
			$dp[ww][0] = d
			$dp[ww][1] = 1
		end
		return d
	end 
end
EOS
puts max f(1,0,0,0),f(0,0,0,0)