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D - Simple Knapsack

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.

4 6
2 1
3 4
4 10
3 4

11

The first and third items should be selected.

4 6
2 1
3 7
4 10
3 6

13

The second and fourth items should be selected.

4 10
1 100
1 100
1 100
1 100

400

You can take everything.

4 1
10 100
10 100
10 100
10 100

0

You can take nothing.