Problem:
Score : 100 points

Problem Statement

There are N items, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Item i has a weight of w_i and a value of v_i.

Taro has decided to choose some of the N items and carry them home in a knapsack.
The capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.

Find the maximum possible sum of the values of items that Taro takes home.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq W \leq 10^9

1 \leq w_i \leq W

1 \leq v_i \leq 10^3

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 sum of the values of items that Taro takes home.

Sample Input 1

3 8
3 30
4 50
5 60

Sample Output 1

90

Items 1 and 3 should be taken.
Then, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.

Sample Input 2

1 1000000000
1000000000 10

Sample Output 2

10

Sample Input 3

6 15
6 5
5 6
6 4
6 6
3 5
7 2

Sample Output 3

17

Items 2, 4 and 5 should be taken.
Then, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17.

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use std::collections::HashMap;
use std::io;
use std::str;

pub struct Scanner<R> {
    reader: R,
    buffer: Vec<String>,
}

impl<R: io::BufRead> Scanner<R> {
    pub fn new(reader: R) -> Self {
        Self {
            reader,
            buffer: vec![],
        }
    }

    pub fn token<T: str::FromStr>(&mut self) -> T {
        loop {
            if let Some(token) = self.buffer.pop() {
                return token.parse().ok().expect("Failed parse");
            }
            let mut input = String::new();
            self.reader.read_line(&mut input).expect("Failed read");
            self.buffer = input.split_whitespace().rev().map(String::from).collect();
        }
    }

    pub fn tokens<T: str::FromStr>(&mut self) -> Vec<T> {
        assert!(self.buffer.is_empty());
        let mut input = String::new();
        self.reader.read_line(&mut input).expect("Failed read");
        input
            .split_whitespace()
            .map(|x| x.parse().ok().expect("Failed parse"))
            .collect()
    }
}

fn pull_dp(n: usize, max_weight: usize, weights: &[i64], values: &[i64]) -> i64 {
    let mut dp = vec![0; max_weight + 1];
    for i in 0..n {
        let mut new_dp = vec![0; max_weight + 1];
        for w in 0..=max_weight {
            new_dp[w] = dp[w];
            if (w as i64) - weights[i] >= 0 {
                new_dp[w] = new_dp[w].max(dp[w - weights[i] as usize] + values[i]);
            }
        }
        dp = new_dp;
    }
    dp[max_weight]
}

fn max_self(a: &mut i64, b: i64) {
    *a = (*a).max(b);
}

fn knapsack(n: usize, max_weight: i64, weights: &[i64], values: &[i64], memo: &mut HashMap<(usize, i64), i64>) -> i64 {
    if n == 0 {
        return 0;
    }
    if let Some(ans) = memo.get(&(n, max_weight)) {
        return *ans;
    }
    let mut ans = knapsack(n - 1, max_weight, weights, values, memo);
    if max_weight >= weights[n - 1] {
        ans = ans.max(knapsack(n - 1, max_weight - weights[n - 1], weights, values, memo) + values[n - 1]);
    }
    memo.insert((n, max_weight), ans);
    ans
}

// f(0, W) = 0
// f(n, W) = f(n - 1, W)
// f(n, W) = f(n - 1, W - weights[n]) + values[n]
fn solve<R: io::BufRead, W: io::Write>(scan: &mut Scanner<R>, out: &mut W) {
    let n: usize = scan.token();
    let max_weight: usize = scan.token();
    let mut weights = Vec::new();
    let mut values = Vec::new();
    for _ in 0..n {
        weights.push(scan.token::<i64>());
        values.push(scan.token::<i64>());
    }
    let mut memo = HashMap::new();
    let ans = knapsack(n, max_weight as i64, &weights, &values, &mut memo);
    writeln!(out, "{}", ans).ok();
}

fn main() {
    let (stdin, stdout) = (io::stdin(), io::stdout());
    let mut scan = Scanner::new(stdin.lock());
    let mut out = io::BufWriter::new(stdout.lock());
    solve(&mut scan, &mut out);
}